# How do you solve -x^2 - 8x + 5 = 0 by completing the square?

Jun 27, 2016

#### Answer:

$x = 0.583 \text{ or } x = - 8.583$

#### Explanation:

The negative ${x}^{2}$ term is not comfortable. Divide by -1.

${x}^{2} + 8 x - 5 = 0$

Move the constant to the other side: $\text{ } {x}^{2} + 8 x = 5$

Add on the square of half the co-efficient of x to both sides to make the square of a binomial.

x^2 + 8x + color(red)16 = 5 + color(red)16 " "color(red)((8/2)^2

${\left(x + 4\right)}^{2} = 21 \text{ square root both sides}$

$x + 4 = \pm \sqrt{21}$

$x = + \sqrt{21} - 4 \text{ or } x = - \sqrt{21} - 4$

$x = 0.583 \text{ or } x = - 8.583$