SOLUTION: solve sqrt x + 5 = sqrt x^2 - 15

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Question 228692: solve sqrt x + 5 = sqrt x^2 - 15
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B5%29=sqrt%28x%5E2-15%29

Square both sides:
x%2B5=x%5E2+-15

It's quadratic, so set it equal to zero by subtracting x +5 from each side:
0=x%5E2+-x+-15-5
0=x%5E2-x-20
0=%28x-5%29%28x%2B4%29+

There are two solutions:
x= 5 or x=-4

You HAVE TO CHECK the answers:
First solution: x=5
sqrt%285%2B5%29+=+sqrt%2825-15%29
sqrt%2810%29=sqrt%2810%29
It checks!

Second solution: x=-4
sqrt%28-4%2B5%29=sqrt%2816-15%29
sqrt%281%29=sqrt%281%29
It checks!

Both solutions work, x= 5, x=-4.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida