solve for $x$ in the equation $x^2 - 12x + 36 = 90$

$x = 6 \pm 3\sqrt{10}$
$x = 6 \pm 2\sqrt{7}$
$x = 12 \pm 3\sqrt{22}$
$x = 12 \pm 3\sqrt{10}$

Question

solve for $x$ in the equation $x^2 - 12x + 36 = 90$

$x = 6 \pm 3\sqrt{10}$
$x = 6 \pm 2\sqrt{7}$
$x = 12 \pm 3\sqrt{22}$
$x = 12 \pm 3\sqrt{10}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perfect-Square Trinomials", "Square Root Property of Equality" ], "new_concepts": [], "current_concepts": [ "Perfect-Square Trinomials", "Square Root Property of Equality", "Solving Quadratic Equations" ] } ## Factor the perfect-square trinomial $$ \begin{aligned} x^2 - 12x + 36 &= 90 \ (x - 6)^2 &= 90 \end{aligned} $$ ## Apply the square root property of equality $$ \begin{aligned} x - 6 &= \pm\sqrt{90} \ x - 6 &= \pm\sqrt{9 \times 10} \ x - 6 &= \pm3\sqrt{10} \end{aligned} $$ ## Solve for x $$ x = 6 \pm 3\sqrt{10} $$

(A) $x = 6 \pm 3\sqrt{10}$

(B) $x = 6 \pm 2\sqrt{7}$

(C) $x = 12 \pm 3\sqrt{22}$

(D) $x = 12 \pm 3\sqrt{10}$

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

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QUESTION IMAGE

Question

Explanation:

Factor the perfect-square trinomial

Apply the square root property of equality

Solve for x

Answer: