select the correct answer.

solve the equation.

\3x^2 + 24x - 24 = 0\

$x = -2 \pm 4\sqrt{6}$

$x = -4 \pm 2\sqrt{6}$

$x = 4 \pm 2\sqrt{6}$

$x = 2 \pm 4\sqrt{6}$

Question

select the correct answer.

solve the equation.

\3x^2 + 24x - 24 = 0\

$x = -2 \pm 4\sqrt{6}$

$x = -4 \pm 2\sqrt{6}$

$x = 4 \pm 2\sqrt{6}$

$x = 2 \pm 4\sqrt{6}$

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", "Algebraic Rearrangement" ], "new_concepts": [], "current_concepts": [ "Quadratic Functions", "Quadratic Formula Application", "Algebraic Rearrangement" ] } ## Divide the equation by the greatest common divisor $$ \begin{aligned} 3x^2 + 24x - 24 &= 0 \ x^2 + 8x - 8 &= 0 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-8 \pm \sqrt{8^2 - 4(1)(-8)}}{2(1)} \ x &= \frac{-8 \pm \sqrt{64 + 32}}{2} \ x &= \frac{-8 \pm \sqrt{96}}{2} \end{aligned} $$ ## Simplify the radical expression $$ \begin{aligned} \sqrt{96} &= \sqrt{16 \times 6} = 4\sqrt{6} \ x &= \frac{-8 \pm 4\sqrt{6}}{2} \ x &= -4 \pm 2\sqrt{6} \end{aligned} $$

(A) $x = -2 \pm 4\sqrt{6}$

(B) $x = -4 \pm 2\sqrt{6}$

(C) $x = 4 \pm 2\sqrt{6}$

(D) $x = 2 \pm 4\sqrt{6}$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Divide the equation by the greatest common divisor

Apply the quadratic formula

Simplify the radical expression

Answer: