SOLUTION: Square root of xraise2 + 5x + 22 + square root of xraise2-5x+6=6

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Question 847238: Square root of xraise2 + 5x + 22 + square root of xraise2-5x+6=6
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%5E2%2B5x%2B22%29+%2B+sqrt%28x%5E2-5x%2B6%29+=+6
square both sides.

2x%5E2+%2B28+%2B+2%2Asqrt%28%28x%5E2%2B5x%2B22%29%28x%5E2-5x%2B6%29%29+=+36
x%5E2+%2B14+%2B+sqrt%28%28x%5E2%2B5x%2B22%29%28x%5E2-5x%2B6%29%29+=+18
sqrt%28%28x%5E2%2B5x%2B22%29%28x%5E2-5x%2B6%29%29+=+%284-x%5E2%29
Square both sides.
%28x%5E2%2B5x%2B22%29%28x%5E2-5x%2B6%29+=+%284-x%5E2%29%5E2
x%5E4%2B3x%5E2-80x%2B132+=+x%5E4-8x%5E2%2B16
3x%5E2-80x+%2B+132+=+-8x%5E2+%2B+16
11x%5E2+-80x+%2B116+=+0
%2880+%2B-+sqrt%28%28-80%29%5E2+-+4%2A11%2A116%29%29%2F22
+x=2 +x+=+58%2F11
Since we are dealing with square roots, it may be a good idea to check our answers to see that we aren't getting extraneous answers.
sqrt%28x%5E2%2B5x%2B22%29+%2B+sqrt%28x%5E2-5x%2B6%29+=+6
When we plug in 2 we get sqrt(36) + sqrt(0) = 6
When we plug in 58/11 we get sqrt(9216/121) + sqrt(900/121) = 11.45.. which is not 6.
That means the only answer that works is x=2.