Question 76668
Solve for x:
{{{sqrt(2x) - sqrt(3x+1) = 1}}} First, add{{{sqrt(3x+1)}}} to both sides of the equation.
{{{sqrt(2x) = sqrt(3x+1) + 1}}} Now square both sides.
{{{2x = (3x+1) + 2sqrt(3x+1) + 1}}} Then, simplify this so that the radical is on one side by itself by subtracting 3x from both sides.
{{{-x = 2sqrt(3x+1) + 2}}} Subtract 2 from both sides.
{{{-x-2 = 2sqrt(3x+1)}}} Now square both sides. {{{(-x-2)^2 = x^2+4x+4}}}
{{{x^2+4x+4 = 4(3x+1)}}} Simplify.
{{{x^2+4x+4 = 12x+4}}} Subtract 12x from both sides.
{{{x^2-8x+4 = 4}}} Subtract 4 from both sides.
{{{x^2-8x = 0}}} Factor an x.
{{{x(x-8) = 0}}} Apply the zero product principle. (If A*B = 0, then either A = 0, or B = 0, or both)
{{{x = 0}}} and/or {{{x-8 = 0}}}
So, {{{x = 0}}} or {{{x = 8}}}