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

$x = 1$ or $5$

$x = -1$ or $7$

$x = 11$

$x = 7$

Question

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

$x = 1$ or $5$

$x = -1$ or $7$

$x = 11$

$x = 7$

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": [ "Linear Equation Solving", "Algebraic Simplification" ], "new_concepts": [ "Solving Quadratic Equations by Square Roots" ], "current_concepts": [ "Linear Equation Solving", "Algebraic Simplification", "Solving Quadratic Equations by Square Roots" ] } ## Isolate the squared term Using the **Algebraic Simplification** 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 To solve for the expression inside the square, we take the square root of both sides. This yields two possible cases: $$ x - 3 = \pm\sqrt{16} $$ $$ x - 3 = \pm 4 $$ ## Solve the resulting linear equations Using the **Linear Equation Solving** knowledge point $$ \begin{aligned} x - 3 = 4 \quad &\Rightarrow \quad x = 7 \ x - 3 = -4 \quad &\Rightarrow \quad x = -1 \end{aligned} $$

$x = 1$ or $5$

$x = -1$ or $7$

$x = 11$

$x = 7$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Isolate the squared term

Apply the square root property

Solve the resulting linear equations

Answer: