How do you solve x^2+ 7x = - 10?

May 9, 2016

The solutions are:

$x = - 2$

$x = - 5$

Explanation:

${x}^{2} + 7 x = - 10$

${x}^{2} + 7 x + 10 = 0$

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

$a = 1 , b = 7 , c = 10$

The Discriminant is given by:

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

$= {\left(7\right)}^{2} - \left(4 \cdot 1 \cdot 10\right)$

$= 49 - 40 = 9$

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

$x = \frac{\left(- 7\right) \pm \sqrt{9}}{2 \cdot 1} = \frac{\left(- 7 \pm \sqrt{9}\right)}{2}$

$x = \frac{- 7 \pm 3}{2}$

$x = \frac{- 7 + 3}{2} = - \frac{4}{2} = - 2$

$x = \frac{- 7 - 3}{2} = - \frac{10}{2} = - 5$