solve for x using the quadratic formula.

\5x^2 - 15x + 10 = 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.

\5x^2 - 15x + 10 = 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", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Quadratic Formula", "Solving Quadratic Functions" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula", "Solving Quadratic Functions" ] } ## Identify the coefficients Using the **Solving Quadratic Functions** knowledge point $$ \begin{aligned} &5x^2 - 15x + 10 = 0\ &a = 5,\quad b = -15,\quad c = 10 \end{aligned} $$ ## Apply the quadratic formula Using the **Quadratic Formula** knowledge point $$ \begin{aligned} x &= \frac{-(-15) \pm \sqrt{(-15)^2 - 4(5)(10)}}{2(5)}\ x &= \frac{15 \pm \sqrt{225 - 200}}{10}\ x &= \frac{15 \pm \sqrt{25}}{10}\ x &= \frac{15 \pm 5}{10} \end{aligned} $$ ## Calculate the solutions Using the **Solving Quadratic Functions** knowledge point $$ \begin{aligned} x_1 &= \frac{15 - 5}{10} = \frac{10}{10} = 1\ x_2 &= \frac{15 + 5}{10} = \frac{20}{10} = 2 \end{aligned} $$ Solve for x using the quadratic formula. $5x^2 - 15x + 10 = 0$ $x =$ 1, 2 Enter the smallest solution first. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula" ] }

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Explanation:

Identify the coefficients

Apply the quadratic formula

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