SOLUTION: I have been trying to figure this out. I couldn't do it the conventional way, but I did find the answer doing guess and check. Please help me find the right way to solve it. {{{ s

Algebra ->  Radicals -> SOLUTION: I have been trying to figure this out. I couldn't do it the conventional way, but I did find the answer doing guess and check. Please help me find the right way to solve it. {{{ s      Log On


   

Question 76685: I have been trying to figure this out. I couldn't do it the conventional way, but I did find the answer doing guess and check. Please help me find the right way to solve it.
+sqrt%28+x%2B14+%29+-+sqrt%28+x-10+%29+= 2
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
I have been trying to figure this out. I couldn't do it the conventional way, but I did find the answer doing guess and check. Please help me find the right way to solve it.
+sqrt%28+x%2B14+%29+-+sqrt%28+x-10+%29+= 2
sqrt%28x%2B14%29-sqrt%28x-10%29%2Bsqrt%28x-10%29=2%2Bsqrt%28x-10%29
sqrt%28x%2B14%29=2%2Bsqrt%28x-10%29
%28sqrt%28x%2B14%29%29%5E2=%282%2Bsqrt%28x-10%29%29%5E2
x%2B14=%282%2Bsqrt%28x-10%29%29%282%2Bsqrt%28x-10%29%29
x%2B14=4%2B2sqrt%28x-10%29%2B2sqrt%28x-10%29%2Bsqrt%28x-10%29%5E2
x%2B14=4%2B4sqrt%28x-10%29%2Bx-10
x%2B14=4sqrt%28x-10%29%2Bx-6
x-x%2B14%2B6=4sqrt%28x-10%29%2Bx-x-6%2B6
20=4sqrt%28x-10%29
20%2F4=4sqrt%28x-10%29%2F4
5=sqrt%28x-10%29
%285%29%5E2=sqrt%28x-10%29%5E2
25=x-10
25%2B10=x-10%2B10
35=x
Check to make sure it's not extraneous:
sqrt%2835%2B14%29-sqrt%2835-10%29=2
sqrt%2849%29-sqrt%2825%29=2
7-5=2
2=2 It's valid:
highlight%28x=35%29
Happy Calculating!!!!