# How do you solve x^2 - 4x = 5 by completing the square?

May 15, 2015

${x}^{2} - 4 x = 5$
To write the Left Hand Side as a Perfect Square, we add 4 to both sides:

${x}^{2} - 4 x + 4 = 5 + 4$

${x}^{2} - 2.2 . x + {2}^{2} = 9$
${x}^{2} - 2.2 . x + {2}^{2} = {3}^{2}$

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

$x - 2 = \sqrt{9}$ or $x - 2 = - \sqrt{9}$

color(green)(x = sqrt 9 +2  or  color(green)(x = -sqrt 9 + 2