solve for x using the quadratic formula.

\2x^2 + 19x - 33 = 0\

\x = ?, \frac{\quad}{\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 + 19x - 33 = 0\

\x = ?, \frac{\quad}{\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 $$ a = 2,\quad b = 19,\quad c = -33 $$ ## Apply quadratic formula $$ \begin{aligned} x &= \frac{-19 \pm \sqrt{19^2 - 4(2)(-33)}}{2(2)} \ x &= \frac{-19 \pm \sqrt{361 + 264}}{4} \ x &= \frac{-19 \pm \sqrt{625}}{4} \ x &= \frac{-19 \pm 25}{4} \end{aligned} $$ ## Calculate solutions $$ \begin{aligned} x_1 &= \frac{-19 - 25}{4} = \frac{-44}{4} = -11 \ x_2 &= \frac{-19 + 25}{4} = \frac{6}{4} = \frac{3}{2} \end{aligned} $$ Solve for x using the quadratic formula. $$2x^2 + 19x - 33 = 0$$ $x =$ -11, $\frac{3}{2}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula" ] }

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Identify coefficients

Apply quadratic formula

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