# How do you solve x^2 + 7x – 1 = 0?

Sep 11, 2015

The solutions are
color(blue)(x= (-7+sqrt(53))/2
color(blue)(x= (-7-sqrt(53))/2

#### Explanation:

The equation : ${x}^{2} + 7 x - 1 = 0$ is of the form color(blue)(ax^2+bx+c=0 where:

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

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$
$= {\left(7\right)}^{2} - \left(4 \cdot \left(1\right) \cdot - 1\right)$
$= 49 + 4 = 53$

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

$x = \frac{- 7 \pm \sqrt{53}}{2 \cdot 1} = \frac{- 7 \pm \sqrt{53}}{2}$

The solutions are
color(blue)(x= (-7+sqrt(53))/2
color(blue)(x= (-7-sqrt(53))/2