select the correct answer.

solve the following equation by completing the square.

\4x^2 - 16x + 8 = 0\

$x = 4$ or $x = 0$

$x = 2 + \sqrt{2}$ or $x = -2 + \sqrt{2}$

$x = -2 + \sqrt{2}$ or $x = -2 - \sqrt{2}$

$x = 2 + \sqrt{2}$ or $x = 2 - \sqrt{2}$

Question

select the correct answer.

solve the following equation by completing the square.

\4x^2 - 16x + 8 = 0\

$x = 4$ or $x = 0$

$x = 2 + \sqrt{2}$ or $x = -2 + \sqrt{2}$

$x = -2 + \sqrt{2}$ or $x = -2 - \sqrt{2}$

$x = 2 + \sqrt{2}$ or $x = 2 - \sqrt{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Completing the Square" ], "new_concepts": [], "current_concepts": [ "Completing the Square", "Quadratic Equations" ] } ## Divide the equation by the leading coefficient $$ \begin{aligned} 4x^2 - 16x + 8 &= 0 \ x^2 - 4x + 2 &= 0 \end{aligned} $$ ## Complete the square $$ \begin{aligned} x^2 - 4x &= -2 \ x^2 - 4x + 4 &= -2 + 4 \ (x - 2)^2 &= 2 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x - 2 &= \pm\sqrt{2} \ x &= 2 \pm \sqrt{2} \end{aligned} $$

(A) $x = 4$ or $x = 0$

(B) $x = 2 + \sqrt{2}$ or $x = -2 + \sqrt{2}$

(C) $x = -2 + \sqrt{2}$ or $x = -2 - \sqrt{2}$

(D) $x = 2 + \sqrt{2}$ or $x = 2 - \sqrt{2}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Completing the Square" ] }

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QUESTION IMAGE

Question

Explanation:

Divide the equation by the leading coefficient

Complete the square

Solve for x

Answer: