question 11 (3 points)

solve. express as exact answers.

\2x^2 + 12x = -5\

Question

question 11 (3 points)

solve. express as exact answers.

\2x^2 + 12x = -5\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Quadratic Formula", "Simplifying Radicals" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Quadratic Formula", "Simplifying Radicals" ] } ## Write the quadratic equation in standard form $$ 2x^2 + 12x + 5 = 0 $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-12 \pm \sqrt{12^2 - 4(2)(5)}}{2(2)} \ x &= \frac{-12 \pm \sqrt{144 - 40}}{4} \ x &= \frac{-12 \pm \sqrt{104}}{4} \end{aligned} $$ ## Simplify the radical and the fraction $$ \begin{aligned} \sqrt{104} &= \sqrt{4 \times 26} = 2\sqrt{26} \ x &= \frac{-12 \pm 2\sqrt{26}}{4} \ x &= \frac{-6 \pm \sqrt{26}}{2} \end{aligned} $$ $x = \frac{-6 \pm \sqrt{26}}{2}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Write the quadratic equation in standard form

Apply the quadratic formula

Simplify the radical and the fraction

Answer: