using the quadratic formula to solve $5x = 6x^2 - 3$, what are the values of $x$?

$\frac{5 \pm 3\sqrt{11}}{12}$

$\frac{5 \pm \sqrt{97}}{12}$

$\frac{5 \pm \sqrt{47}}{12}$

$\frac{-5 \pm \sqrt{97}}{12}$

Question

using the quadratic formula to solve $5x = 6x^2 - 3$, what are the values of $x$?

$\frac{5 \pm 3\sqrt{11}}{12}$

$\frac{5 \pm \sqrt{97}}{12}$

$\frac{5 \pm \sqrt{47}}{12}$

$\frac{-5 \pm \sqrt{97}}{12}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations" ], "new_concepts": [ "Quadratic Formula Application" ], "current_concepts": [ "Solving Quadratic Equations", "Quadratic Formula Application" ] } ## Rearrange the equation into standard form $$ \begin{aligned} 5x &= 6x^2 - 3 \ 0 &= 6x^2 - 5x - 3 \end{aligned} $$ ## Identify coefficients for the quadratic formula $$ \begin{aligned} a &= 6 \ b &= -5 \ c &= -3 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-5) \pm \sqrt{(-5)^2 - 4(6)(-3)}}{2(6)} \ x &= \frac{5 \pm \sqrt{25 + 72}}{12} \ x &= \frac{5 \pm \sqrt{97}}{12} \end{aligned} $$

(A) $\frac{5 \pm 3\sqrt{11}}{12}$

(B) $\frac{5 \pm \sqrt{97}}{12}$

(C) $\frac{5 \pm \sqrt{47}}{12}$

(D) $\frac{-5 \pm \sqrt{97}}{12}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Rearrange the equation into standard form

Identify coefficients for the quadratic formula

Apply the quadratic formula

Answer: