How do you solve $x^{2} - 7 x - 6 = 0$ $x^2-7x-6=0$ using the quadratic formula?

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How do you solve $x^{2} - 7 x - 6 = 0$ $x^2-7x-6=0$ using the quadratic formula?

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Answer 1 · 2015-08-10T02:34:25

$x = \frac{7 + \sqrt{73}}{2}$ $x=(7+sqrt(73))/(2)$ or $x = \frac{7 - \sqrt{73}}{2}$ $x=(7-sqrt(73))/(2)$

Explanation:

The quadratic formula states that for a quadratic equation $a x^{2} + b x + c$ $ax^2+bx+c$ , its roots, $x$ $x$ can be computed as $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x = (-b+-sqrt(b^2-4ac))/(2a)$

Consider the quadratic equation $x^{2} - 7 x - 6 = 0$ $x^2-7x-6=0$ . It has coefficients $a = 1$ $a=1$ , $b = - 7$ $b=-7$ and $c = - 6$ $c=-6$ . To solve for $x$ $x$ , we plug these numbers into the quadratic formula.

$x = \frac{- (- 7) \pm \sqrt{{(- 7)}^{2} - 4 (1) (- 6)}}{2 (1)}$ $x = (-(-7)+-sqrt((-7)^2-4(1)(-6)))/(2(1))$
$x = \frac{7 \pm \sqrt{73}}{2}$ $x = (7+-sqrt(73))/(2)$

Hence, $x = \frac{7 + \sqrt{73}}{2}$ $x=(7+sqrt(73))/(2)$ or $x = \frac{7 - \sqrt{73}}{2}$ $x=(7-sqrt(73))/(2)$

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How do you solve $x^{2} - 7 x - 6 = 0$ $x^2-7x-6=0$ using the quadratic formula?

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