# How do you solve sqrt(x -1) = x - 3?

Apr 25, 2018

x=2,5

#### Explanation:

To remove the square root, square both sides

$x - 1 = {\left(x - 3\right)}^{2}$

Square the right side

${\left(x - 3\right)}^{2} = \left(x - 3\right) \left(x - 3\right) = {x}^{2} - 3 x - 3 x + 9$

$x - 1 = {x}^{2} - 6 x + 9$

Combine terms and set equation to 0

$0 = {x}^{2} - 7 x + 10$

Factor

$0 = \left(x - 2\right) \left(x - 5\right)$