what are the solutions of (8x^2 = 6 + 22x)? check all of the boxes that apply

(x = -3)

(x = -\frac{1}{4})

(x = 3)

(x = 6)

Question

what are the solutions of (8x^2 = 6 + 22x)? check all of the boxes that apply

(x = -3)

(x = -\frac{1}{4})

(x = 3)

(x = 6)

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", "Zeros of Quadratic Functions" ] } ## Rearrange the quadratic equation into standard form $$ \begin{aligned} 8x^2 &= 22x + 6 \ 8x^2 - 22x - 6 &= 0 \ 2(4x^2 - 11x - 3) &= 0 \ 4x^2 - 11x - 3 &= 0 \end{aligned} $$ ## Factor the quadratic expression $$ \begin{aligned} 4x^2 - 12x + x - 3 &= 0 \ 4x(x - 3) + 1(x - 3) &= 0 \ (4x + 1)(x - 3) &= 0 \end{aligned} $$ ## Solve for the roots $$ \begin{aligned} 4x + 1 = 0 &\implies x = -\frac{1}{4} \ x - 3 = 0 &\implies x = 3 \end{aligned} $$

$x = -3$

$x = -\frac{1}{4}$

$x = 3$

$x = 6$

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

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QUESTION IMAGE

Question

Explanation:

Rearrange the quadratic equation into standard form

Factor the quadratic expression

Solve for the roots

Answer: