SOLUTION: Please sove this square root function equation. I know the answer is 9, but I don't know how √(x-5)+√(x)=5

Algebra ->  Radicals -> SOLUTION: Please sove this square root function equation. I know the answer is 9, but I don't know how √(x-5)+√(x)=5      Log On


   

Question 845821: Please sove this square root function equation. I know the answer is 9, but I don't know how
√(x-5)+√(x)=5
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-5%29%5E%281%2F2%29%2Bx%5E%281%2F2%29=5

Square it once:
%28x-5%29%2B2%28x-5%29%5E%281%2F2%29x%5E%281%2F2%29%2Bx=25
2%2Asqrt%28x%28x-5%29%29=25-%28x-5%29-x
2%2Asqrt%28x%5E2-5x%29=25-x%2B5-x
2%2Asqrt%28x%5E2-5x%29=30-2x
sqrt%28x%5E2-5x%29=15-x

Square this once more:
x%5E2-5x=%2815-x%29%5E2
x%5E2-5x=15%5E2-30x%2Bx%5E2
-5x=15%5E2-30x
25x=15%5E2
25x=3%2A5%2A3%2A5
highlight%28x=9%29