How do you solve $2 x^{2} - 13 x - 7 = 0$ $2x^2-13x-7=0$ using the quadratic formula?

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How do you solve $2 x^{2} - 13 x - 7 = 0$ $2x^2-13x-7=0$ using the quadratic formula?

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Answer 1 · 2017-04-16T14:56:47

$x = 7$ $x=7$ or $x = - \frac{1}{2}$ $x=-1/2$

Explanation:

Let's begin with the quadratic formula: $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x=(-b+- sqrt(b^2-4ac))/(2a$

In the equation $2 x^{2} - 13 x - 7 = 0$ $2x^2 - 13x - 7 = 0$ , the a-value equals 2, the b-value equals -13, and the c-value is -7.

We substitute those numbers into our equation, and simplify to find our answer:

$x = \frac{13 \pm \sqrt{169 - 4 (2) (- 7)}}{2 (2)}$ $x=(13+-sqrt(169-4(2)(-7)))/(2(2))$ (Substitution)
$x = \frac{13 \pm \sqrt{225}}{4}$ $x=(13+- sqrt(225))/(4)$ (Simplify)
$x = \frac{13 \pm 15}{4}$ $x=(13+-15)/4$ (Simplify)
$x = \frac{28}{4}$ $x=(28)/4$ or $x = \frac{- 2}{4}$ $x=(-2)/4$ (Simplify)
$x = 7$ $x=7$ or $x = - \frac{1}{2}$ $x=-1/2$ (Simplify)

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How do you solve $2 x^{2} - 13 x - 7 = 0$ $2x^2-13x-7=0$ using the quadratic formula?

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How do you solve $2 x^{2} - 13 x - 7 = 0$ $2x^2-13x-7=0$ using the quadratic formula?