use the quadratic formula to solve: $x^2 + 7x - 8 = 0$

$x =$

or $x =$

Question

use the quadratic formula to solve: $x^2 + 7x - 8 = 0$

$x =$

or $x =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations" ], "new_concepts": [ "Quadratic Formula" ], "current_concepts": [ "Quadratic Equations", "Quadratic Formula" ] } ## Identify coefficients from the quadratic equation $$ \begin{aligned} &a = 1 \ &b = 7 \ &c = -8 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-7 \pm \sqrt{7^2 - 4(1)(-8)}}{2(1)} \ x &= \frac{-7 \pm \sqrt{49 + 32}}{2} \ x &= \frac{-7 \pm \sqrt{81}}{2} \ x &= \frac{-7 \pm 9}{2} \end{aligned} $$ ## Calculate the two solutions $$ \begin{aligned} x_1 &= \frac{-7 + 9}{2} = \frac{2}{2} = 1 \ x_2 &= \frac{-7 - 9}{2} = \frac{-16}{2} = -8 \end{aligned} $$ Use the quadratic formula to solve: $x^2+7x-8=0$ $x =$ $1$ or $x =$ $-8$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients from the quadratic equation

Apply the quadratic formula

Calculate the two solutions

Answer: