what is the solution to (2x^2+8x=x^2-16)?

(x=-4)
(x=-2)
(x=2)
(x=4)

Question

what is the solution to (2x^2+8x=x^2-16)?

(x=-4)
(x=-2)
(x=2)
(x=4)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Quadratic Equations", "Factoring Quadratics" ], "current_concepts": [ "Quadratic Equations", "Factoring Quadratics" ] } ## Rearrange the equation into standard form $$ \begin{aligned} 2x^2 + 8x &= x^2 - 16 \ 2x^2 - x^2 + 8x + 16 &= 0 \ x^2 + 8x + 16 &= 0 \end{aligned} $$ ## Factor the quadratic equation $$ \begin{aligned} (x + 4)^2 &= 0 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x + 4 &= 0 \ x &= -4 \end{aligned} $$

(A) $x = -4$

(B) $x = -2$

(C) $x = 2$

(D) $x = 4$

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

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QUESTION IMAGE

Question

Explanation:

Rearrange the equation into standard form

Factor the quadratic equation

Solve for x

Answer: