How do you solve x^2 + 6x – 7 = 0 using the quadratic formula?

Apr 14, 2016

$x = 1$
$x = - 7$

Explanation:

Given-

${x}^{2} + 7 x - 7 = 0$
${x}^{2} + 7 x - x - 7 = 0$
$x \left(x + 7\right) - 1 \left(x + 7\right) = 0$
$\left(x - 1\right) \left(x + 7\right)$
$x - 1 = 0$
$x = 1$

$x + 7 = 0$
$x = - 7$

Apr 14, 2016

The solutions are:

$x = 1$

$x = - 7$

Explanation:

${x}^{2} + 6 x - 7 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:

$a = 1 , b = 6 , c = - 7$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(6\right)}^{2} - \left(4 \cdot 1 \cdot \left(- 7\right)\right)$

$= 36 + 28 = 64$

The solutions are normally found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{\left(- 6\right) \pm \sqrt{64}}{2 \cdot 1} = \frac{- 6 \pm 8}{2}$

$x = \frac{- 6 + 8}{2} = \frac{2}{2} = 1$

$x = \frac{- 6 - 8}{2} = - \frac{14}{2} = - 7$