# How do you solve 30^ { 2} + x ^ { 2} = 36^ { 2}?

May 7, 2017

Simplify, then take the square root. $x = \pm 6 \sqrt{11}$

#### Explanation:

First, simplify it.
${30}^{2} = 900$ and ${36}^{2} = 1296$

So now you have $900 + {x}^{2} = 1296$

Now, get the x by itself. You can do that by subtracting 900 from both sides.

$900 - 900 + {x}^{2} = 1296 - 900$
$0 + {x}^{2} = 396$
${x}^{2} = 396$

You would then have to take the square root of each side to make ${x}^{2}$ just x. However, 396 is not a perfect square, so you would simplify it as much as you could if you didn't have a calculator:

±sqrt(396)
=±sqrt(36*11)
=±sqrt(6*6*11)
=±6sqrt(11)
~~±19.9 (found with calculator)