Question 48021
Solve for x:
{{{sqrt(x-1) = x-7}}} First, square both sides of the equation.
{{{x-1 = x^2-14x+49}}} Subtract x from both sides.
{{{-1 = x^2-15x+49}}} Now add 1 to both sides.
{{{0 = x^2-15x+50}}} Factor the right side.
{{{0 = (x-5)(x-10)}}} Apply the zero products principle.
{{{x-5 = 0}}} and/or{{{x-10 = 0}}}
If {{{x-5 = 0}}} then {{{x = 5}}}
If {{{x-10 = 0}}} the {{{x = 10}}}

The roots are:
x = 5
x = 10