select the correct answer.

solve the equation using the method of completing the square.

(2x^2 + 16x - 8 = 0)

(x = 2 pm 4sqrt{5})
(x = 4 pm 2sqrt{5})
(x = -2 pm 4sqrt{5})
(x = -4 pm 2sqrt{5})

Question

select the correct answer.

solve the equation using the method of completing the square.

(2x^2 + 16x - 8 = 0)

(x = 2 pm 4sqrt{5})
(x = 4 pm 2sqrt{5})
(x = -2 pm 4sqrt{5})
(x = -4 pm 2sqrt{5})

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", "Quadratic Functions" ], "new_concepts": [], "current_concepts": [ "Completing the Square", "Quadratic Functions" ] } ## Divide the equation by the leading coefficient $$ \begin{aligned} 2x^2 + 16x - 8 &= 0 \ x^2 + 8x - 4 &= 0 \end{aligned} $$ ## Complete the square $$ \begin{aligned} x^2 + 8x &= 4 \ x^2 + 8x + 16 &= 4 + 16 \ (x + 4)^2 &= 20 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x + 4 &= \pm\sqrt{20} \ x + 4 &= \pm2\sqrt{5} \ x &= -4 \pm 2\sqrt{5} \end{aligned} $$

(A) $x = 2 \pm 4\sqrt{5}$

(B) $x = 4 \pm 2\sqrt{5}$

(C) $x = -2 \pm 4\sqrt{5}$

(D) $x = -4 \pm 2\sqrt{5}$

{ "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: