4. solve: $4(x - 3)^2 = 64$

$x = 11$

$x = 1$ or $5$

$x = -1$ or $7$

$x = 7$

Question

4. solve: $4(x - 3)^2 = 64$

$x = 11$

$x = 1$ or $5$

$x = -1$ or $7$

$x = 7$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations by Square Roots", "Linear Equation Solving" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations by Square Roots", "Linear Equation Solving" ] } ## Isolate the squared term Using the **Solving Quadratic Equations by Square Roots** knowledge point $$ \begin{aligned} 4(x - 3)^2 &= 64 \ (x - 3)^2 &= \frac{64}{4} \ (x - 3)^2 &= 16 \end{aligned} $$ ## Apply the square root property Using the **Solving Quadratic Equations by Square Roots** knowledge point $$ \begin{aligned} x - 3 &= \pm\sqrt{16} \ x - 3 &= \pm 4 \end{aligned} $$ ## Solve for x Using the **Linear Equation Solving** knowledge point $$ \begin{aligned} x &= 3 \pm 4 \ x_1 &= 3 - 4 = -1 \ x_2 &= 3 + 4 = 7 \end{aligned} $$

(A) $x = 11$

(B) $x = 1 or 5$

(C) $x = -1 or 7$

(D) $x = 7$

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

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QUESTION IMAGE

Question

Explanation:

Isolate the squared term

Apply the square root property

Solve for x

Answer: