Question 80094
Solve for x:
{{{sqrt(2x+6)-sqrt(x-6) = 3}}} First, isolate the radicals if possible. Here, you can add {{{sqrt(x-6)}}} to both sides.
{{{sqrt(2x+6) = sqrt(x-6)+3}}} Now square both sides to remove the radicals, well...some of them.
{{{2x+6 = x-6+6sqrt(x-6)+9}}} Simplify this. Subtract x from both sides.
{{{x+6 = 6sqrt(x-6)+3}}} Subtract 3 from both sides.
{{{x+3= 6sqrt(x-6)}}} Square both sides again to remove the remaining radical.
{{{x^2+6x+9 = 36(x-6)}}} Simplify.
{{{x^2+6x+9 = 36x-216}}} Subtract 36x from both sides.
{{{x^2-30x+9 = -216}}} Add 216 to both sides.
{{{x^2-30x+225 = 0}}} Now factor this quadratic equation.
{{{(x-15)(x-15) = 0}}} Apply the zero products principle.
{{{x-15 = 0}}} Add 15 to both sides.
{{{x = 15}}}
Your teacher is correct!