# How do you solve 1-sqrt( 7-x)= x?

Apr 16, 2016

$x = - 2 \text{ or } x = + 3$

#### Explanation:

It is matter of reversing the actions given and doing so in the correct order.

Write as:$\text{ } 1 - x = \sqrt{7 - x}$

Square both sides

${\left(1 - x\right)}^{2} = 7 - x$

${x}^{2} - 2 x + 1 = 7 - x$

${x}^{2} - x - 6 = 0$

$\left(x + 2\right) \left(x - 3\right) = 0$

$x = - 2 \text{ or } x = + 3$