# How do you solve x^2 - 18x = 19 by completing the square?

Jul 13, 2015

Solve: $y = {x}^{2} - 18 x - 19 = 0$

#### Explanation:

Since (a - b + c = 0), use the shortcut. The 2 real roots are: (- 1) and (-c/a = 19).

Solving by completing the squares

${x}^{2} - 18 x + 81 = 19 + 81 = 100$
${\left(x - 9\right)}^{2} = 100$ --> $x - 9 = \pm 10$
$x = 9 \pm 10$ --> x = - 1 and x = 19.