# How do you solve f^2 - 18f + 70 = -8 by completing the square?

##### 1 Answer
May 13, 2016

The solutions are:
color(green)(f= sqrt 3 + 9  ,  color(green)(f = -sqrt 3 +9

#### Explanation:

${f}^{2} - 18 f + 70 = - 8$

${f}^{2} - 18 f = - 78$

To write the Left Hand Side as a Perfect Square, we add 81 to both sides:

${f}^{2} - 18 f + 81 = - 78 + 81$

${f}^{2} - 2 \cdot f \cdot 9 + {9}^{2} = 3$

Using the Identity color(blue)((a-b)^2 = a^2 - 2ab + b^2, we get
${\left(f - 9\right)}^{2} = 3$

$f - 9 = \sqrt{3}$ or $f - 9 = - \sqrt{3}$

color(green)(f= sqrt 3 + 9  ,  color(green)(f = -sqrt 3 +9