solve for x using the quadratic formula.

\4x^2 - 63x + 98 = 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.

\4x^2 - 63x + 98 = 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 $$ a = 4, \quad b = -63, \quad c = 98 $$ ## Apply quadratic formula $$ \begin{aligned} x &= \frac{-(-63) \pm \sqrt{(-63)^2 - 4(4)(98)}}{2(4)} \ x &= \frac{63 \pm \sqrt{3969 - 1568}}{8} \ x &= \frac{63 \pm \sqrt{2401}}{8} \ x &= \frac{63 \pm 49}{8} \end{aligned} $$ ## Calculate solutions $$ \begin{aligned} x_1 &= \frac{63 - 49}{8} = \frac{14}{8} = \frac{7}{4} \ x_2 &= \frac{63 + 49}{8} = \frac{112}{8} = 14 \end{aligned} $$ Solve for x using the quadratic formula. $$4x^2 - 63x + 98 = 0$$ $x =$ $\frac{7}{4}$ , $14$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula" ] }

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Question

Explanation:

Identify coefficients

Apply quadratic formula

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