福音原則第10章單字表

 

英文字詞	KK 音標	字詞原形	詞性 (繁體中文)	中文翻譯 (取自《福音原則》中文版)	難度等級
ancient	[ˈen.ʃənt]	ancient	形容詞	古代的、古老的	B2
compile	[kəmˈpaɪl]	compile	動詞	彙編、編纂	B2
contain	[kənˈteɪn]	contain	動詞	包含、收錄	B1
doctrine	[ˈdɑk.trɪn]	doctrine	名詞	教義、教理	B2
edify	[ˈɛ.də.faɪ]	edify	動詞	建立德行、啟迪	B2
enlighten	[ɪnˈlaɪ.tən]	enlighten	動詞	啟發、使明白	B2
everlasting	[ˌɛv.ɚˈlæst.ɪŋ]	everlasting	形容詞	永恆的、永存的	B2
guidance	[ˈɡaɪ.dəns]	guide	名詞 (由動詞衍生)	引導、指引	B2
knowledge	[ˈnɑ.lɪdʒ]	knowledge	名詞	知識	B1
preserve	[prɪˈzɝv]	preserve	動詞	保存、維護	B2
prophecy	[ˈprɑ.fə.si]	prophecy	名詞	預言（內容）、先知之言	B2
record	[ˈrɛk.ɚd] (n) / [rɪˈkɔrd] (v)	record	名詞／動詞	記載、紀錄	B1/B2
revelation	[ˌrɛv.əˈleɪ.ʃən]	reveal	名詞	啟示	B2
scripture	[ˈskrɪp.tʃɚ]	scripture	名詞	經文（尤指標準經文）	B2
valuable	[ˈvæl.ju.ə.bəl]	valuable	形容詞	有價值的、寶貴的	B2

Absolut Phrase 獨立片語

 Analyze the sentence's syntax: In order to stand, the true Church must be “built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone”

ChatGPT 說：

Let's analyze the syntax of the sentence:

"In order to stand, the true Church must be 'built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone.'"

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1. Sentence Type & Structure

• This is a complex declarative sentence with:
  • A main clause.
  • An infinitive phrase ("In order to stand") as an adverbial modifier.
  • A passive verb phrase ("must be built").
  • A participle phrase ("Jesus Christ himself being the chief corner stone") as an additional descriptive element.

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2. Clause Breakdown

Adverbial Infinitive Phrase (Purpose)

• "In order to stand,"
  • "In order to" → Prepositional phrase introducing purpose.
  • "stand" → Bare infinitive verb, expressing the goal or necessity.
  • This phrase functions adverbially, explaining why the true Church must be built a certain way.

Main Clause

• "The true Church must be built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone."

  • Subject → "The true Church" (noun phrase).
  • Modal Verb → "must" (expresses necessity).
  • Passive Verb Phrase → "be built" (passive voice, indicating that the Church is the recipient of the action).
  • Prepositional Phrase → "upon the foundation of the apostles and prophets" (modifies "be built," specifying where/how the Church is built).

Absolute Phrase (Descriptive)

• "Jesus Christ himself being the chief corner stone"
  • This phrase is an absolute construction, consisting of:
    • Noun Phrase → "Jesus Christ himself" (who is being described).
    • Present Participle → "being" (describes the role of Jesus Christ).
    • Noun Phrase (Complement) → "the chief corner stone" (renames "Jesus Christ").
  • The absolute phrase adds extra information, reinforcing that Christ is central to the foundation.

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3. Function of the Components

✔ "In order to stand" (adverbial phrase of purpose) → Explains why the Church must be built on the foundation.
✔ "The true Church must be built upon the foundation of the apostles and prophets" (main clause) → Expresses a necessary condition for the Church’s stability.
✔ "Jesus Christ himself being the chief corner stone" (absolute phrase) → Further clarifies the essential role of Christ in the foundation.

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4. Key Syntactic Features

• Passive Voice: "Must be built" suggests that the Church is acted upon rather than performing the action itself.
• Infinitive Phrase for Purpose: "In order to stand" explains the necessity of the foundation.
• Prepositional Phrase for Location: "Upon the foundation of the apostles and prophets" describes where the Church is built.
• Absolute Phrase for Additional Description: "Jesus Christ himself being the chief corner stone" functions as an extra detail, almost like a side note, but essential to the meaning.

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Final Interpretation

✔ The main idea is that the true Church must be built on a strong foundation in order to endure.
✔ Jesus Christ is emphasized as the key element in this foundation.
✔ The sentence follows a clear logical structure: purpose (why) → necessity (what must happen) → further clarification (who is central to this foundation).

Would you like more examples of similar biblical structures? 😊

你說：

Is "Jesus Christ himself being the chief corner stone" an adverbial phrase?

ChatGPT 說：

No, "Jesus Christ himself being the chief corner stone" is not an adverbial phrase. Instead, it functions as an absolute phrase, which is different from an adverbial phrase in structure and function. Let’s analyze why.

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1. What is an Absolute Phrase?

An absolute phrase consists of:

1. A noun or pronoun (in this case, "Jesus Christ himself").
2. A participle (present or past) (in this case, "being").
3. A complement that describes the noun (in this case, "the chief corner stone").

2. How Absolute Phrases Function

• Absolute phrases do not directly modify any single word in the main clause.
• Instead, they provide additional information about the entire sentence, often expressing cause, condition, or circumstance.

Comparison with an Adverbial Phrase

• An adverbial phrase modifies a verb, adjective, or another adverb by answering how, when, where, why, or under what condition something happens.
• "Jesus Christ himself being the chief corner stone" does not answer any of these adverbial questions about the verb "must be built."
• Instead, it adds descriptive information about the foundation, reinforcing Jesus Christ’s role in it.

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3. How "Jesus Christ himself being the chief corner stone" Functions in the Sentence

• It does not modify the verb "must be built."
• It describes the state of Jesus Christ in relation to the foundation.
• It functions similarly to a nonrestrictive appositive phrase, clarifying the basis of the Church's foundation.

🔹 Example of a True Adverbial Phrase for Comparison:

• "In order to stand" is an adverbial phrase because it modifies "must be built," explaining why the Church must be built on a strong foundation.

🔹 Example of an Absolute Phrase for Comparison:

• "The sun having set, we returned home."
  • ("The sun having set" describes the situation under which "we returned home.")
• Similarly, "Jesus Christ himself being the chief corner stone" provides background information, not a direct modification of the verb.

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4. Conclusion

✔ "Jesus Christ himself being the chief corner stone" is an absolute phrase, not an adverbial phrase.
✔ It adds additional information about Jesus Christ’s role in the foundation but does not modify the main verb ("must be built").
✔ The phrase functions independently, providing descriptive context rather than modifying the action.

Would you like more examples of absolute phrases in biblical or formal writing? 😊

給定一個陳述句，列舉可能的疑問句。

這一句話可以造出幾個問句，請列舉所有問句，並簡答這些問句，然後把回答翻譯成中文，與英文並列: Many people find it easy to believe in the prophets of the past.

一般疑問句 (Yes/No Questions)

1. Do many people find it easy to believe in the prophets of the past?
   許多人覺得相信過去的先知很容易嗎？
   → Yes, they do. / No, they don’t.
   → 是的，他們覺得容易。/ 不，他們不覺得容易。

2. Is it easy for many people to believe in the prophets of the past?
   對許多人來說，相信過去的先知很容易嗎？
   → Yes, it is. / No, it isn’t.
   → 是的，很容易。/ 不，不容易。

---

選擇疑問句 (Choice Questions)
3. Do many people find it easy or difficult to believe in the prophets of the past?
許多人覺得相信過去的先知很容易還是很困難？
→ They find it easy. / They find it difficult.
→ 他們覺得容易。/ 他們覺得困難。

4. Is it easy for many people to believe in the prophets of the past, or do they struggle with it?
   對許多人來說，相信過去的先知很容易，還是他們覺得困難？
   → It is easy for them. / They struggle with it.
   → 對他們來說很容易。/ 他們覺得困難。

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特殊疑問句 (Wh- Questions)
5. Who finds it easy to believe in the prophets of the past?
誰覺得相信過去的先知很容易？
→ Many people.
→ 許多人。

6. What do many people find easy?
   許多人覺得什麼事情很容易？
   → Believing in the prophets of the past.
   → 相信過去的先知。

7. What do many people believe in easily?
   許多人很容易相信什麼？
   → The prophets of the past.
   → 過去的先知。

8. Why do many people find it easy to believe in the prophets of the past?
   為什麼許多人覺得相信過去的先知很容易？
   → Because of their faith/history/tradition.
   → 因為他們的信仰/歷史/傳統。

9. When do many people find it easy to believe in the prophets of the past?
   許多人在什麼時候覺得相信過去的先知很容易？
   → When they read scriptures/hear stories/etc.
   → 當他們閱讀經文/聽故事/等等時。

10. How do many people find it easy to believe in the prophets of the past?
    許多人是如何覺得相信過去的先知很容易的？
    → Through faith/study/testimony.
    → 透過信仰/學習/見證。

11. In whom do many people find it easy to believe?
    許多人覺得容易相信誰？
    → The prophets of the past.
    → 過去的先知。

12. What kind of prophets do many people find it easy to believe in?
    許多人覺得容易相信哪種類型的先知？
    → The prophets of the past.
    → 過去的先知。

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反身疑問句 (Tag Questions)
13. Many people find it easy to believe in the prophets of the past, don’t they?
許多人覺得相信過去的先知很容易，不是嗎？
→ Yes, they do. / No, they don’t.
→ 是的，他們覺得容易。/ 不，他們不覺得容易。

福音原則第9章單字表

 

英文字詞	KK 音標	字詞原形	詞性 (繁體中文)	中文翻譯 (取自《福音原則》中文版)	難度等級
apostasy	[əˈpɑ.stə.si]	apostasy	名詞	叛教、背道	B2
authority	[əˈθɔr.ə.ti]	authority	名詞	權柄、權威	B2
condemnation	[ˌkɑn.dəmˈneɪ.ʃən]	condemn	名詞	定罪、譴責	B2
counsel	[ˈkaʊn.səl]	counsel	名詞／動詞	勸告、指導；商議	B2
declare	[dɪˈklɛr]	declare	動詞	宣告、聲明	B2
distort	[dɪˈstɔrt]	distort	動詞	扭曲、曲解	B2
fulfill	[fʊlˈfɪl]	fulfill	動詞	實現、履行	B2
heed	[hid]	heed	動詞	注意、留心	B2
interpret	[ɪnˈtɝ.prɪt]	interpret	動詞	解釋、詮釋	B2
ordain	[ɔrˈdeɪn]	ordain	動詞	任命（聖職）、授予（權柄）	B2
preserve	[prɪˈzɝv]	preserve	動詞	保存、維護	B2
proclaim	[proʊˈkleɪm]	proclaim	動詞	宣佈、宣揚	B2
prophet	[ˈprɑ.fɪt]	prophet	名詞	先知	B1/B2
prophecy	[ˈprɑ.fə.si]	prophecy	名詞	預言（內容）、先知之言	B2
rebellious	[rɪˈbɛl.jəs]	rebellious	形容詞	叛逆的、反叛的	B2
revelation	[ˌrɛv.əˈleɪ.ʃən]	reveal	名詞	啟示	B2
spokesman	[ˈspoʊks.mən]	spokesman	名詞	發言人	B2
testify	[ˈtɛs.tə.faɪ]	testify	動詞	見證、作證	B2
unchanging	[ˌʌnˈtʃeɪn.dʒɪŋ]	unchanging	形容詞	永恆不變的	B2
witness	[ˈwɪt.nəs]	witness	動詞／名詞	見證；證人	B2

福音原則第8章單字表

 福音原則第8章單字表

英文字詞	KK 音標	字詞原形	詞性 (繁體中文)	中文翻譯 (取自《福音原則》中文版)	難度等級
address	[əˈdrɛs]	address	動詞	稱呼、向…講話（禱告時的稱呼）	B2
blessing	[ˈblɛs.ɪŋ]	blessing	名詞	祝福、恩典	B1
communicate	[kəˈmju.nə.keɪt]	communicate	動詞	溝通	B2
communication	[kəˌmju.nəˈkeɪ.ʃən]	communication	名詞	溝通、交流	B2
commune	[kəˈmjun]	commune	動詞	親近、交心（在禱告中與神溝通）	B2
consistent	[kənˈsɪs.tənt]	consistent	形容詞	一致的、持續不斷的	B2
counsel	[ˈkaʊn.səl]	counsel	名詞／動詞	勸告、建議；商議	B2
demonstrate	[ˈdɛm.ən.streɪt]	demonstrate	動詞	展現、示範	B2
expression	[ɪkˈsprɛʃ.ən]	expression	名詞	表達、表露	B2
formal	[ˈfɔr.məl]	formal	形容詞	正式的、莊重的	B2
gratitude	[ˈɡræ.tə.tud]	gratitude	名詞	感恩、感激	B2
guidance	[ˈɡaɪ.dəns]	guide	名詞 (衍生自動詞)	指引、引導	B2
humble	[ˈhʌm.bəl]	humble	形容詞	謙卑的	B2
humility	[hjuˈmɪl.ə.ti]	humility	名詞	謙卑	B2
individually	[ˌɪn.dəˈvɪdʒ.u.ə.li]	individual	副詞 (衍生用法)	個別地、單獨地	B2
kneel	[nil]	kneel	動詞	跪下	B1
opportunity	[ˌɑ.pɚˈtu.nə.ti]	opportunity	名詞	機會	B1
pattern	[ˈpæt.ɚn]	pattern	名詞	模式、範例	B2
petition	[pəˈtɪʃ.ən]	petition	名詞	祈求、請願	B2
posture	[ˈpɑs.tʃɚ]	posture	名詞	姿勢（如禱告時的肢體動作）	B2
pour	[pʊr]	pour	動詞	傾訴、傾倒（向神敞開心扉）	B1/B2
private	[ˈpraɪ.vɪt]	private	形容詞	私下的、個人的	B2
reverence	[ˈrɛv.ɚ.əns]	reverence	名詞	敬畏、崇敬	B2
sincere	[sɪnˈsɪr]	sincere	形容詞	真誠的	B2
sincerely	[sɪnˈsɪr.li]	sincere	副詞 (衍生用法)	真誠地、誠懇地	B2
supplication	[ˌsʌp.lɪˈkeɪ.ʃən]	supplicate	名詞	懇求、祈求	B2
thankful	[ˈθæŋk.fəl]	thankful	形容詞	感激的	B1
worship	[ˈwɝ.ʃɪp]	worship	動詞／名詞	敬拜、崇拜	B2

福音原則第7章單字表

 

英文字詞	KK 音標	字詞原形	詞性 (繁體中文)	中文翻譯 (取自《福音原則》中文版)	難度等級
accompany	[əˈkʌm.pə.ni]	accompany	動詞	陪伴、伴隨	B2
administer	[ədˈmɪn.ə.stɚ]	administer	動詞	施行、執行	B2
advocate	[ˈæd.və.keɪt]	advocate	名詞／動詞	辯護者、倡導；主張	B2
baptize	[bæpˈtaɪz]	baptize	動詞	為…施洗	B1/B2
baptism	[ˈbæp.tɪ.zəm]	baptism	名詞	洗禮	B2
comforter	[ˈkʌm.fɚ.tɚ]	comforter	名詞	慰助者（此處多指「聖靈」的稱號之一）	B2
companionship	[kəmˈpæn.jən.ʃɪp]	companionship	名詞	作伴、陪伴	B2
confirm	[kənˈfɝm]	confirm	動詞	堅定、確認	B1/B2
confirmation	[ˌkɑn.fɚˈmeɪ.ʃən]	confirmation	名詞	確認、堅定禮（教義語境常指堅定禮）	B2
constant	[ˈkɑn.stənt]	constant	形容詞	持續不斷的、恆久的	B2
counsel	[ˈkaʊn.səl]	counsel	名詞／動詞	勸告、指導；商議	B2
discern	[dɪˈsɝn]	discern	動詞	分辨、洞察	B2
divine	[dəˈvaɪn]	divine	形容詞	神聖的、來自神的	B2
entice	[ɪnˈtaɪs]	entice	動詞	誘惑、引誘	B2
essential	[ɪˈsɛn.ʃəl]	essential	形容詞	必要的、不可或缺的	B2
ghost	[ɡoʊst]	ghost	名詞	靈、幽靈（此處多指「聖靈」的意涵）	B1/B2
gift	[ɡɪft]	gift	名詞	恩賜、禮物（此章多指「聖靈的恩賜」）	B1
godhead	[ˈɡɑd.hɛd]	godhead	名詞	神格（神性三位一體之概念）	B2
guidance	[ˈɡaɪ.dəns]	guide	名詞 (由動詞衍生)	指引、引導	B2
holy	[ˈhoʊ.li]	holy	形容詞	神聖的	B2
influence	[ˈɪn.flu.əns]	influence	名詞／動詞	影響、感化	B2
inspire	[ɪnˈspaɪr]	inspire	動詞	啟發、感召	B2
manifest	[ˈmæn.ə.fɛst]	manifest	動詞	顯現、表明	B2
obedience	[oʊˈbi.di.əns]	obedience	名詞	順服、服從	B2
ordinance	[ˈɔr.dən.əns]	ordinance	名詞	教儀、聖禮	B2
overcome	[ˌoʊ.vɚˈkʌm]	overcome	動詞	克服、戰勝	B2
presence	[ˈprɛ.zəns]	presence	名詞	臨在、存在	B2
priesthood	[ˈpristhʊd]	priesthood	名詞	聖職（神職權能）	B2
prompt	[prɑmpt]	prompt	動詞／形容詞	促使；迅速的	B2
quicken	[ˈkwɪk.ən]	quicken	動詞	使活躍、使甦醒	B2
receive	[rɪˈsiv]	receive	動詞	接受、領受	B1
relationship	[rɪˈleɪ.ʃən.ʃɪp]	relationship	名詞	關係、聯繫	B2
reveal	[rɪˈvil]	reveal	動詞	顯示、啟示	B2
righteous	[ˈraɪ.tʃəs]	righteous	形容詞	公義的、正直的	B2
sacred	[ˈseɪ.krɪd]	sacred	形容詞	神聖的	B2
testify	[ˈtɛs.tə.faɪ]	testify	動詞	見證、作證	B2
transgression	[trænzˈɡrɛʃ.ən]	transgress	名詞	過犯、違背	B2
unrighteous	[ˌʌnˈraɪ.tʃəs]	unrighteous	形容詞	不義的、不公的	B2
warn	[wɔrn]	warn	動詞	警告、告誡	B1
withdraw	[wɪðˈdrɔ]	withdraw	動詞	撤回、退卻	B2
witness	[ˈwɪt.nəs]	witness	動詞／名詞	見證；證人	B2
worthy	[ˈwɝ.ði]	worthy	形容詞	配稱的、值得…的	B2
worthily	[ˈwɝ.ði.li]	worthy	副詞 (衍生用法)	值得地、配得地	B2

多項式，已知餘數，求商

 

We are given the function:

$$f(x) = (4x^2 - 2x + 1)(mx + n) + 4x - 9$$

with the conditions:

$$f\left(-\frac{1}{2}\right) = -5, \quad f(1) = -8.$$

We need to determine $m$ and $n$, and then compute $f(2)$.

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Step 1: Compute $f(-\frac{1}{2})$

Substituting $x = -\frac{1}{2}$:

$$4\left(-\frac{1}{2}\right)^2 - 2\left(-\frac{1}{2}\right) + 1 = 4\left(\frac{1}{4}\right) + 1 + 1 = 1 + 1 + 1 = 3.$$
$$f\left(-\frac{1}{2}\right) = (3)(m(-\frac{1}{2}) + n) + 4(-\frac{1}{2}) - 9$$
$$= 3\left(-\frac{m}{2} + n\right) - 2 - 9$$
$$= 3n - \frac{3m}{2} - 11$$

Setting this equal to $-5$:

$$3n - \frac{3m}{2} - 11 = -5$$
$$3n - \frac{3m}{2} = 6$$
$$3n = \frac{3m}{2} + 6$$
$$n = \frac{m}{2} + 2$$

---

Step 2: Compute $f(1)$

Substituting $x = 1$:

$$4(1)^2 - 2(1) + 1 = 4 - 2 + 1 = 3.$$
$$f(1) = 3(m(1) + n) + 4(1) - 9$$
$$= 3(m + n) + 4 - 9$$
$$= 3m + 3n - 5$$

Setting this equal to $-8$:

$$3m + 3n - 5 = -8$$
$$3m + 3n = -3$$
$$m + n = -1$$

---

Step 3: Solve for $m$ and $n$

We have the system:

1. $n = \frac{m}{2} + 2$
   
2. $m + n = -1$
   

Substituting equation (1) into equation (2):

$$m + \left(\frac{m}{2} + 2\right) = -1$$
$$m + \frac{m}{2} + 2 = -1$$

Multiply everything by 2 to clear the fraction:

$$2m + m + 4 = -2$$
$$3m = -6$$
$$m = -2$$

Substituting $m = -2$ into $n=\frac{m}{2}+\mathrm{2:}$

$$n = \frac{-2}{2} + 2 = -1 + 2 = 1$$

Thus, we have:

$$m = -2, \quad n = 1.$$

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Step 4: Compute $f(2)$

Substituting $x = 2$:

$$4(2)^2 - 2(2) + 1 = 16 - 4 + 1 = 13.$$
$$f(2) = (13)(m(2) + n) + 4(2) - 9$$
$$= 13(-2(2) + 1) + 8 - 9$$
$$= 13(-4 + 1) + 8 - 9$$
$$= 13(-3) + 8 - 9$$
$$= -39 + 8 - 9$$
$$= -40$$

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Final Answer

$$\boxed{{\displaystyle -40}}$$

多項式，x 位移

 

Yes! Let's perform continuous synthetic division step by step until we get the Nested Division Form of

$$3x^3 - 5x^2 - 7x - 4$$

divided by $x-3.$

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Step 1: First Synthetic Division

We divide $3x^3 - 5x^2 - 7x - 4$ using synthetic division.

Set Up the Synthetic Division Table

1. Write the coefficients of the polynomial: $$3, -5, -7, -4$$
   
2. The divisor is $x - 3$, so we use $\mathrm{3\; as\; the\; synthetic\; division\; factor.}$

$$\begin{array}{r|rrrr} 3 & 3 & -5 & -7 & -4 \\ & & 9 & 12 & 15 \\ \hline & 3 & 4 & 5 & 11 \\ \end{array}$$

• Quotient: $3x^2+4x+5$
• Remainder: $11$
  

Thus, we now divide $3x^2+4x+5.$

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Step 2: Second Synthetic Division

Now, divide $3x^2+4x+5.$

$$\begin{array}{r|rrr} 3 & 3 & 4 & 5 \\ & & 9 & 39 \\ \hline & 3 & 13 & 44 \\ \end{array}$$

• Quotient: $3x+13$
• Remainder: $44$

Now, divide $3x + 13$ by $x - 3$.

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Step 3: Third Synthetic Division

Now, divide $3x + 13$ by $x-3.$

$$\begin{array}{r|rr} 3 & 3 & 13 \\ & & 9 \\ \hline & 3 & 22 \\ \end{array}$$

• Quotient: $3$
  
• Remainder: $22$
  

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Step 4: Express in Nested Division Form

Now, we reconstruct the polynomial using the results of the synthetic divisions.

1. The final quotient is 3.

2. The previous quotient was $3x+\mathrm{13,\; which\; we\; write\; as:}$

   $$3(x - 3) + 22$$

3. The next quotient was $3x^2 + 4x + 5$, which we write using the previous step:

   $$3(x - 3)^2 + 22(x - 3) + 44$$

4. Finally, including the remainder:

   $$3(x - 3)^3 + 22(x - 3)^2 + 44(x - 3) + 11$$
   

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Final Answer:

$$\boxed{3(x - 3)^3 + 22(x - 3)^2 + 44(x - 3) + 11}$$

This is the Nested Division Form of $3x^3 - 5x^2 - 7x - 4$ when divided by $x - 3$.

多項式，替換新變數

 

We are given the equation:

$$(x^2 - 3x)^2 - 14(x^2 - 3x) + 40 = 0$$

Step 1: Substituting a New Variable

Let:

$$y = x^2 - 3x$$

Then, our equation transforms into:

$$y^2 - 14y + 40 = 0$$

Step 2: Solve the Quadratic Equation

The quadratic equation:

$$y^2 - 14y + 40 = 0$$

can be solved using the quadratic formula:

$$y = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(1)(40)}}{2(1)}$$ $$y = \frac{14 \pm \sqrt{196 - 160}}{2}$$ $$y = \frac{14 \pm \sqrt{36}}{2}$$ $$y = \frac{14 \pm 6}{2}$$

Step 3: Find Values of $y$

$$y = \frac{14 + 6}{2} = \frac{20}{2} = 10$$
$$y = \frac{14 - 6}{2} = \frac{8}{2} = 4$$

Thus, we have two equations to solve:

$$x^2 - 3x = 10$$
$$x^2 - 3x = 4$$

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Step 4: Solve for $x$

Equation 1: $x^2-3x-10=0$

Factorizing:

$$(x - 5)(x + 2) = 0$$
$$x - 5 = 0 \quad \text{or} \quad x + 2 = 0$$
$$x = 5 \quad \text{or} \quad x = -2$$

Equation 2: $x^2-3x-4=0$

Factorizing:

$$(x - 4)(x + 1) = 0$$
$$x - 4 = 0 \quad \text{or} \quad x + 1 = 0$$
$$x = 4 \quad \text{or} \quad x = -1$$

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Final Answer

$$\boxed{{\displaystyle x=5,-2,4,-1}}$$