Question 6739
Solve:
{{{sqrt(5x+6)-sqrt(3x-2) = 2}}} Add {{{sqrt(3x-2)}}} to both sides.
{{{sqrt(5x+6) = 2 + sqrt(3x-2)}}} Square both sides.
{{{(5x+6) = 4 + 4sqrt(3x-2) + (3x-2)}}} Simplify.
{{{5x+6 = 2 + 3x + 4sqrt(3x-2)}}} Subtract 3x from both sides.
{{{2x+6 = 2 + 4sqrt(3x-2)}}} Subtract 2 from both sides.
{{{2x+4 = 4sqrt(3x-2)}}} Square both sides.
{{{4x^2 + 16x + 16 = 16(3x-2)}}} Simplify.
{{{4x^2 + 16x + 16 = 48x - 32}}} Subtract 48x from both sides.
{{{4x^2 - 32x + 16 = -32}}} Add 32 to both sides.
{{{4x^2 - 32x + 48 = 0}}} Divide both sides by 4.
{{{x^2 - 8x + 12 = 0}}} Solve by factoring.
{{{(x - 2)(x - 6) = 0}}} Apply the zero product principle.

x - 2 = 0, x = 2 or
x - 6 = 0, x = 6