what are the solutions of $x^2 + 6x - 6 = 10$?

$x = -11$ or $x = 1$
$x = -11$ or $x = -1$
$x = -8$ or $x = -2$
$x = -8$ or $x = 2$

Question

what are the solutions of $x^2 + 6x - 6 = 10$?

$x = -11$ or $x = 1$
$x = -11$ or $x = -1$
$x = -8$ or $x = -2$
$x = -8$ or $x = 2$

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", "Factoring Quadratics" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Factoring Quadratics" ] } ## Rearrange the quadratic equation into standard form $$ \begin{aligned} x^2 + 6x - 6 &= 10 \ x^2 + 6x - 16 &= 0 \end{aligned} $$ ## Factor the quadratic expression $$ \begin{aligned} (x + 8)(x - 2) = 0 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x + 8 = 0 &\implies x = -8 \ x - 2 = 0 &\implies x = 2 \end{aligned} $$

$x = -11$ or $x = 1$

$x = -11$ or $x = -1$

$x = -8$ or $x = -2$

$x = -8$ or $x = 2$

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

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Explanation:

Rearrange the quadratic equation into standard form

Factor the quadratic expression

Solve for x

Answer: