SOLUTION: the question says solve: 2X+6 (under a square root)- X-6(under a square root)=3 My teacher got X=15 but I can not figure out how he came to that conclusion, could you help me plea

Algebra ->  Radicals -> SOLUTION: the question says solve: 2X+6 (under a square root)- X-6(under a square root)=3 My teacher got X=15 but I can not figure out how he came to that conclusion, could you help me plea      Log On


   

Question 80094: the question says solve: 2X+6 (under a square root)- X-6(under a square root)=3
My teacher got X=15 but I can not figure out how he came to that conclusion, could you help me please?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
sqrt%282x%2B6%29-sqrt%28x-6%29+=+3 First, isolate the radicals if possible. Here, you can add sqrt%28x-6%29 to both sides.
sqrt%282x%2B6%29+=+sqrt%28x-6%29%2B3 Now square both sides to remove the radicals, well...some of them.
2x%2B6+=+x-6%2B6sqrt%28x-6%29%2B9 Simplify this. Subtract x from both sides.
x%2B6+=+6sqrt%28x-6%29%2B3 Subtract 3 from both sides.
x%2B3=+6sqrt%28x-6%29 Square both sides again to remove the remaining radical.
x%5E2%2B6x%2B9+=+36%28x-6%29 Simplify.
x%5E2%2B6x%2B9+=+36x-216 Subtract 36x from both sides.
x%5E2-30x%2B9+=+-216 Add 216 to both sides.
x%5E2-30x%2B225+=+0 Now factor this quadratic equation.
%28x-15%29%28x-15%29+=+0 Apply the zero products principle.
x-15+=+0 Add 15 to both sides.
x+=+15
Your teacher is correct!