Question 77353
Solve for x: Hint: Isolate the radical.
{{{sqrt(3x+1)-1 = x-4}}} First, add 1 to both sides of the equation.
{{{sqrt(3x+1) = x-3}}} Now square both sides.
{{{3x+1 = x^2-6x+9}}} Next, subtract 3x from both sides.
{{{1 = x^2-9x+9}}} Now subtract 1 from both sides.
{{{0 = x^2-9x+8}}} or:
{{{x^2-9x+8 = 0}}} Solve this quadratic equation by factoring.
{{{(x-8)(x-1) = 0}}} Apply the zero products principle:
{{{x-8 = 0}}} or {{{x-1 = 0}}}
The solutions:
{{{x = 8}}}
{{{x = 1}}}