solve for x using the quadratic formula.

\2x^2 + 6x - 36 = 0\

\x = ?, \quad \

enter the smallest solution first.

quadratic formula: \x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\

Question

solve for x using the quadratic formula.

\2x^2 + 6x - 36 = 0\

\x = ?, \quad \

enter the smallest solution first.

quadratic formula: \x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Formula" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula", "Solving Quadratic Functions" ] } ## Identify coefficients from the quadratic equation $$ \begin{aligned} &2x^2 + 6x - 36 = 0\ &a = 2,\quad b = 6,\quad c = -36 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\ x &= \frac{-6 \pm \sqrt{6^2 - 4(2)(-36)}}{2(2)}\ x &= \frac{-6 \pm \sqrt{36 + 288}}{4}\ x &= \frac{-6 \pm \sqrt{324}}{4}\ x &= \frac{-6 \pm 18}{4} \end{aligned} $$ ## Calculate the two solutions $$ \begin{aligned} x_1 &= \frac{-6 - 18}{4} = \frac{-24}{4} = -6\ x_2 &= \frac{-6 + 18}{4} = \frac{12}{4} = 3 \end{aligned} $$ Solve for x using the quadratic formula. $$2x^2 + 6x - 36 = 0$$ $x =$ -6, 3 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients from the quadratic equation

Apply the quadratic formula

Calculate the two solutions

Answer: