# How do you complete the square to solve x^2 - 2x - 35 = 0?

May 25, 2015

$0 = {x}^{2} - 2 x - 35$

$= {x}^{2} - 2 x + 1 - 1 - 35$

$= {\left(x - 1\right)}^{2} - 36$

$= {\left(x - 1\right)}^{2} - {6}^{2}$

$= \left(\left(x - 1\right) - 6\right) \left(\left(x - 1\right) + 6\right)$

$= \left(x - 7\right) \left(x + 5\right)$

So $x = 7$ or $x = - 5$

I used the difference of squares inequality along the way:

$\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$