Question 144547
{{{sqrt(-2x-7) + sqrt(x+9)= sqrt(8-x)}}} Start with the given equation



{{{(sqrt(-2x-7) + sqrt(x+9))^2= (sqrt(8-x))^2}}} Square both sides



{{{(sqrt(-2x-7))^2 + 2*sqrt(-2x-7)*sqrt(x+9)+ (sqrt(x+9))^2= 8-x}}} Foil



{{{-2x-7 + 2*sqrt(-2x-7)*sqrt(x+9)+ x+9= 8-x}}} Square and multiply



{{{-2x-7 + 2*sqrt((-2x-7)*(x+9))+ x+9= 8-x}}} Combine the square roots



{{{-2x-7 + 2*sqrt(-2x^2-25x-63)+ x+9= 8-x}}} Foil



{{{2*sqrt(-2x^2-25x-63)- x+2= 8-x}}} Combine like terms



{{{2*sqrt(-2x^2-25x-63)= 8-x+x-2}}} Add x to both sides. Subtract 2 from both sides. 



{{{2*sqrt(-2x^2-25x-63)= 6}}}  Combine like terms



{{{sqrt(-2x^2-25x-63)= 3}}}  Divide both sides by 2



{{{(sqrt(-2x^2-25x-63))^2= (3)^2}}}  Square both sides



{{{-2x^2-25x-63= 9}}}  Simplify



{{{-2x^2-25x-63-9=0}}}  Subtract 25 from both sides. 



{{{-2x^2-25x-72=0}}} Combine like terms




{{{(-x-8)(2x+9)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{-x-8=0}}} or  {{{2x+9=0}}} 


{{{x=-8}}} or  {{{x=-9/2}}}    Now solve for x in each case



So our answers are


 {{{x=-8}}} or  {{{x=-9/2}}}