# How do you factor x^2+11=300?

Sep 16, 2015

$\left(x + 17\right) \left(x - 17\right) = 0$

#### Explanation:

Subtract $300$ from both sides

${x}^{2} + 11 - 300 = 300 - 300$

${x}^{2} - 289 = 0$

The left hand side is the difference of two squares.
We factor as follows

$\left(x + 17\right) \left(x - 17\right) = 0$

Or we could say

${x}^{2} = 289$ by subtracting $11$ from both sides

Taking the square root we have

$x = \pm \sqrt{289} = \pm 17$

but you want the factorization so we go with what i did first

Sep 16, 2015

(x-17)(x+17)

#### Explanation:

To factorise this, recollect that ${17}^{2} = 289$

The give expression can be simplified to ${x}^{2} - 300 + 11 = 0$

${x}^{2} - 289 = 0$
$\left({x}^{2} - {17}^{2}\right) = 0$

(x-17)(x+17)=0