# How do you solve x^2 - 6x = 391 by completing the square?

Apr 12, 2016

$x = 23$ or $x - 17$

#### Explanation:

In ${x}^{2} - 6 x = 391$ as the Left Hand Side is ${x}^{2} - 6 x$, we can make it a complete square (compare it with ${\left(x - a\right)}^{2} = {x}^{2} - 2 a x + {a}^{2}$) by adding **square of half the coefficient of $x$.

As coefficient of $x$ is $- 6$, we need to add ${\left(- \frac{6}{2}\right)}^{2} = 9$, to each side and then we have

${x}^{2} - 6 x + 9 = 391 + 9 = 400$

or ${\left(x - 3\right)}^{2} = {20}^{2}$

Hence either $x - 3 = 20$ or $x - 3 = - 20$ i.e.

$x = 23$ or $x - 17$