Question 49955
Solve:
{{{sqrt(x+1) = sqrt(x+6)-1}}} First, square both sides.
{{{x+1 = (x+6)-2sqrt(x+6)+1}}} Simplify.
{{{x+1 = (x+1)+6-2sqrt(x+6)}}} Subtract (x+1) from both sides.
{{{0 = 6-2sqrt(x+6)}}} Add {{{2sqrt(x+6)}}} to both sides.
{{{2sqrt(x+6) = 6}}} Divide both sides by 2.
{{{sqrt(x+6) = 3}}} Now square both sides.
{{{x+6 = 9}}} Finally, subtract 6 from both sides.
{{{x = 3}}}

Check:
{{{sqrt(3+1) = sqrt(3+6)-1}}}
{{{sqrt(4) = sqrt(9)-1}}}
{{{2 = 3-1}}} 
{{{2 = 2}}}