what are the values of x in the equation $x^2 - 6x + 9 = 25$?

$x = -2$ or $x = 8$
$x = -1$ or $x = -11$
$x = 1$ or $x = 11$
$x = 2$ or $x = -8$

Question

what are the values of x in the equation $x^2 - 6x + 9 = 25$?

$x = -2$ or $x = 8$
$x = -1$ or $x = -11$
$x = 1$ or $x = 11$
$x = 2$ or $x = -8$

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", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Perfect-Square Trinomials", "Solving Quadratic Equations" ] } ## Factor the perfect-square trinomial $$ \begin{aligned} x^2 - 6x + 9 &= 25 \ (x - 3)^2 &= 25 \end{aligned} $$ ## Apply the square root property $$ \begin{aligned} x - 3 &= \pm\sqrt{25} \ x - 3 &= \pm 5 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x &= 3 + 5 \implies x = 8 \ x &= 3 - 5 \implies x = -2 \end{aligned} $$

(A) $x = -2$ or $x = 8$

(B) $x = -1$ or $x = -11$

(C) $x = 1$ or $x = 11$

(D) $x = 2$ or $x = -8$

{ "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

Solve for x

Answer: