SOLUTION: {{{ sqrt(x)-sqrt(x-20)=10}}} I know the answer is 36, but I'm not sure how to get the answer.

Algebra ->  Radicals -> SOLUTION: {{{ sqrt(x)-sqrt(x-20)=10}}} I know the answer is 36, but I'm not sure how to get the answer.      Log On


   

Question 651887: +sqrt%28x%29-sqrt%28x-20%29=10
I know the answer is 36, but I'm not sure how to get the answer.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+sqrt%28x%29-sqrt%28x-20%29=10
if the answer is 36, than +sqrt%2836%29-sqrt%2836-20%29=10...->..+6-sqrt%2816%29=10.->..+6-4=10->..+2=10,,,which is not true
you probably made mistake using minus sign
with plus sign you will get:
sqrt%28x%29%2Bsqrt%28x-20%29=10
%28sqrt%28x%29%2Bsqrt%28x-20%29%29%5E2=10%5E2
sqrt%28x%29%5E2%2B2sqrt%28x%29sqrt%28x-20%29%2Bsqrt%28x-20%29%5E2=100
x%2B2sqrt%28x%29sqrt%28x-20%29%2B%28x-20%29=100
2x%2B2sqrt%28x%28x-20%29%29-20=100
2x%2B2sqrt%28x%28x-20%29%29=100%2B20
2sqrt%28x%28x-20%29%29=-2x%2B120
%282sqrt%28x%28x-20%29%29%29%5E2=%28-2x%2B120%29%5E2
4%28x%28x-20%29%29=%28-2x%29%5E2-2%282x%29%2A120%2B120%5E2
4%28x%5E2-20x%29=4x%5E2-480x%2B14400
4x%5E2-80x=4x%5E2-480x%2B14400
cross%284x%5E2%29-80x=cross%284x%5E2%29-480x%2B14400
-80x=-480x%2B14400
-80x%2B480x=14400
400x=14400
x=14400%2F400
x=36