Question 298175
x+1+sqrt(x+4)=9
once I isolate the radical I end up with x+4=(8-X)(8-x) WHat do  I do next.


{{{x + 1 + sqrt(x + 4) = 9}}}


{{{sqrt(x + 4) = 8 - x}}}


x + 4 = (8 - x)(8 - x)------- Square both sides of equation


{{{x + 4 = 64 - 16x + x^2}}} ------ FOILing right-side of equation


{{{0 = x^2 - 17x + 60}}} -------> {{{x^2 - 17x + 60 = 0}}}


(x - 12)(x - 5) = 0


x = 12 or 5


However, when 12 is substituted back into the original equation, we get: 

{{{12 + 1 + sqrt(12+4) = 9}}}

{{{13 + sqrt(16) = 9}}}


{{{13 + 4 <> 9}}}


But, when 5 is substituted back into the original equation, we get: 

{{{5 + 1 + sqrt(5+4) = 9}}}

{{{6 + sqrt(9) = 9}}}


{{{6 + 3 = 9}}}


Therefore, the only solution is {{{highlight_green(x = 5)}}}