SOLUTION: Thank you in advance for helping me with this equation. sqrt(-2x-7) + sqrt(x+9)= sqrt(8-x)

Algebra ->  Radicals -> SOLUTION: Thank you in advance for helping me with this equation. sqrt(-2x-7) + sqrt(x+9)= sqrt(8-x)      Log On


   

Question 144547This question is from textbook
: Thank you in advance for helping me with this equation. sqrt(-2x-7) + sqrt(x+9)= sqrt(8-x) This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28-2x-7%29+%2B+sqrt%28x%2B9%29=+sqrt%288-x%29 Start with the given equation


%28sqrt%28-2x-7%29+%2B+sqrt%28x%2B9%29%29%5E2=+%28sqrt%288-x%29%29%5E2 Square both sides


Foil


-2x-7+%2B+2%2Asqrt%28-2x-7%29%2Asqrt%28x%2B9%29%2B+x%2B9=+8-x Square and multiply


-2x-7+%2B+2%2Asqrt%28%28-2x-7%29%2A%28x%2B9%29%29%2B+x%2B9=+8-x Combine the square roots


-2x-7+%2B+2%2Asqrt%28-2x%5E2-25x-63%29%2B+x%2B9=+8-x Foil


2%2Asqrt%28-2x%5E2-25x-63%29-+x%2B2=+8-x Combine like terms


2%2Asqrt%28-2x%5E2-25x-63%29=+8-x%2Bx-2 Add x to both sides. Subtract 2 from both sides.


2%2Asqrt%28-2x%5E2-25x-63%29=+6 Combine like terms


sqrt%28-2x%5E2-25x-63%29=+3 Divide both sides by 2


%28sqrt%28-2x%5E2-25x-63%29%29%5E2=+%283%29%5E2 Square both sides


-2x%5E2-25x-63=+9 Simplify


-2x%5E2-25x-63-9=0 Subtract 25 from both sides.


-2x%5E2-25x-72=0 Combine like terms



%28-x-8%29%282x%2B9%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
-x-8=0 or 2x%2B9=0

x=-8 or x=-9%2F2 Now solve for x in each case


So our answers are

x=-8 or x=-9%2F2