# How do you solve sqrt(x+1) =sqrt(x-5)?

Mar 23, 2018

No Solution

#### Explanation:

$\sqrt{x + 1} = \sqrt{x - 5}$

In order to eliminate a square root we can square the root.
Whatever you do on the left, you also do on the right.

${\sqrt{x + 1}}^{2} = {\left(\sqrt{x - 5}\right)}^{2}$

This leaves us with the equation

$x + 1 = x - 5$

Combine like terms by using the additive/subtractive inverse.

$\cancel{x} \cancel{+ 1} \cancel{- x} \cancel{- 1} = \cancel{x} - 5 \cancel{- x} - 1$

This leaves

$0 \ne - 6$
No Solution