Question 155522
Solve for x:
{{{sqrt(5x+1) = x-4}}} Square both sides of the equation.
{{{5x+1 = x^2-8x+16}}} Subtract 5x from both sides.
{{{1 = x^2-13x+16}}} Subtract 1 from both sides.
{{{x^2-13x+15 = 0}}} This is not factorable so use the quadratic formula:{{{x = (-b+-sqrt(b^2-4ac))/2a}}} Here, a = 1, b = -13, and c = 15, so make the appropriate substitutions:
{{{x = (-(-13)+-sqrt((-13)^2-4(1)(15)))/2(1)}}} Simplify.
{{{x = (13+-sqrt(169-60))/2}}}
{{{x = (13+-sqrt(109))/2}}}
{{{x = (13+sqrt(109))/2}}} or {{{x = (13-sqrt(109))/2}}}