# How do you solve using the completing the square method z^2 + 10z = -24?

Mar 4, 2016

The solutions are:

color(green)(z = -4
 color(green)(z =-6

#### Explanation:

${z}^{2} + 10 z = - 24$

To write the Left Hand Side as a Perfect Square, we add 25 to both sides
${z}^{2} + 10 z + 25 = - 24 + 25$

${z}^{2} + 2 \cdot 5 \cdot z + {5}^{2} = 1$

Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get
${\left(z + 5\right)}^{2} = 1$

$z + 5 = + \sqrt{1} = 1$
color(green)(z =1 - 5= -4

or,

$z + 5 = - \sqrt{1} = - 1$
color(green)(z = -1 -5=-6