using the quadratic formula to solve (4x^2 - 3x + 9 = 2x + 1), what are the values of (x)?

(\frac{1 pm sqrt{159}i}{8})

(\frac{5 pm sqrt{153}i}{8})

(\frac{5 pm sqrt{103}i}{8})

(\frac{1 pm sqrt{153}}{8})

Question

using the quadratic formula to solve (4x^2 - 3x + 9 = 2x + 1), what are the values of (x)?

(\frac{1 pm sqrt{159}i}{8})

(\frac{5 pm sqrt{153}i}{8})

(\frac{5 pm sqrt{103}i}{8})

(\frac{1 pm sqrt{153}}{8})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula Application", "Solving Quadratic Equations" ] } ## Rearrange the equation into standard form $$ \begin{aligned} 4x^2 - 3x + 9 &= 2x + 1 \ 4x^2 - 5x + 8 &= 0 \end{aligned} $$ ## Identify coefficients and apply the quadratic formula $$ \begin{aligned} a &= 4,\quad b = -5,\quad c = 8 \ x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-5) \pm \sqrt{(-5)^2 - 4(4)(8)}}{2(4)} \end{aligned} $$ ## Simplify the expression $$ \begin{aligned} x &= \frac{5 \pm \sqrt{25 - 128}}{8} \ x &= \frac{5 \pm \sqrt{-103}}{8} \ x &= \frac{5 \pm \sqrt{103}i}{8} \end{aligned} $$

(A) $\frac{1 \pm \sqrt{159}i}{8}$

(B) $\frac{5 \pm \sqrt{153}i}{8}$

(C) $\frac{5 \pm \sqrt{103}i}{8}$

(D) $\frac{1 \pm \sqrt{153}}{8}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula Application" ] }

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QUESTION IMAGE

Question

Explanation:

Rearrange the equation into standard form

Identify coefficients and apply the quadratic formula

Simplify the expression

Answer: