solve for $x$ in the equation $3x^2 - 18x + 5 = 47$

$x = 3 \pm \sqrt{23}$
$x = 3 \pm \sqrt{51}$
$x = 3 \pm \sqrt{41}$
$x = 3 \pm \sqrt{5}$

Question

solve for $x$ in the equation $3x^2 - 18x + 5 = 47$

$x = 3 \pm \sqrt{23}$
$x = 3 \pm \sqrt{51}$
$x = 3 \pm \sqrt{41}$
$x = 3 \pm \sqrt{5}$

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", "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Quadratic Formula Application" ] } ## Rearrange the quadratic equation into standard form $$ \begin{aligned} 3x^2 - 18x + 5 &= 47 \ 3x^2 - 18x - 42 &= 0 \ x^2 - 6x - 14 &= 0 \end{aligned} $$ ## Apply the quadratic formula or complete the square $$ \begin{aligned} x^2 - 6x &= 14 \ x^2 - 6x + 9 &= 14 + 9 \ (x - 3)^2 &= 23 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x - 3 &= \pm\sqrt{23} \ x &= 3 \pm \sqrt{23} \end{aligned} $$

(A) $x = 3 \pm \sqrt{23}$

(B) $x = 3 \pm \sqrt{51}$

(C) $x = 3 \pm \sqrt{41}$

(D) $x = 3 \pm \sqrt{5}$

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

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QUESTION IMAGE

Question

Explanation:

Rearrange the quadratic equation into standard form

Apply the quadratic formula or complete the square

Solve for x

Answer: