# How do you solve x(x - 4) = 45  by completing the square?

May 23, 2016

x = -5 , x= 9

#### Explanation:

Since this is a quadratic equation expand brackets and equate to zero.

$\Rightarrow {x}^{2} - 4 x - 45 = 0$

This is now in standard form : $a {x}^{2} + b x + c = 0$

To complete the square add on ${\left(\frac{b}{2}\right)}^{2}$

here b = -4$\Rightarrow {\left(- \frac{4}{2}\right)}^{2} = 4$

equation can now be written as

$\left[{x}^{2} - 4 x + 4\right] + \left(- 4\right) - 45 = 0$

Since we added on 4 to complete the square we must -4

$\Rightarrow {\left(x - 2\right)}^{2} - 4 - 45 = 0 \Rightarrow {\left(x - 2\right)}^{2} = 49$

Taking the square root of both sides.

x-2=±sqrt49=±7

hence x = 7 + 2 = 9 or x = -7 + 2 =-5