# How do you solve x^2-8x=9 by completing the square?

Jul 7, 2015

Solve y = x^2 - 8x - 9 = 0

#### Explanation:

In this case, you don't need to solve by completing the squares.
Use the shortcut.
When (a - b + c = 0) --> 2 real roots: (-1) and (-c/a = 9).

Jul 7, 2015

You take half the $x$-coefficient ($- 8 \to - 4$) and square it ($16$)

#### Explanation:

This means you have to add $16$ to both sides of the equation:
${x}^{2} - 8 x + 16 = 9 + 16 \to$
${\left(x - 4\right)}^{2} = 25 \to$
So: $x - 4 = \sqrt{25} = 5 \to x = 9$
Or: $x - 4 = - \sqrt{25} = - 5 \to x = - 1$