solve for $x$ in the equation $x^2 + 4x - 4 = 8$

$x = -6$ or $x = 2$
$x = -2 \pm 2\sqrt{2}$
$x = -2$ or $x = 6$
$x = 2 \pm 2\sqrt{2}$

Question

solve for $x$ in the equation $x^2 + 4x - 4 = 8$

$x = -6$ or $x = 2$
$x = -2 \pm 2\sqrt{2}$
$x = -2$ or $x = 6$
$x = 2 \pm 2\sqrt{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations" ] } ## Rearrange the quadratic equation into standard form $$ \begin{aligned} x^2 + 4x - 4 &= 8 \ x^2 + 4x - 12 &= 0 \end{aligned} $$ ## Factor the quadratic equation $$ \begin{aligned} (x + 6)(x - 2) &= 0 \end{aligned} $$ ## Solve for the roots $$ \begin{aligned} x + 6 = 0 &\implies x = -6 \ x - 2 = 0 &\implies x = 2 \end{aligned} $$

(A) $x = -6$ or $x = 2$

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

(C) $x = -2$ or $x = 6$

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

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

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Question

Explanation:

Rearrange the quadratic equation into standard form

Factor the quadratic equation

Solve for the roots

Answer: