SOLUTION: What is the square root of 2x+5 (both under the square root symbol) equals 2+the square root of x-2 (also both under the square root symbol)?

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Question 29608: What is the square root of 2x+5 (both under the square root symbol) equals 2+the square root of x-2 (also both under the square root symbol)?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%282x%2B5%29+=+2+%2B+sqrt%28x-2%29+

Now square both sides:
+%28sqrt%282x%2B5%29%29%5E2+=+%282+%2B+sqrt%28x-2%29%29%5E2+
+%282x%2B5%29+=+%282+%2B+sqrt%28x-2%29%29%282+%2B+sqrt%28x-2%29%29+

+2x%2B5+=+%284+%2B+4sqrt%28x-2%29+%2B+%28x-2%29%29+
+2x%2B5+=+%284+%2B+4sqrt%28x-2%29+%2B+x-2%29+
+x%2B3+=+4sqrt%28x-2%29+

Square both sides again:
+%28x%2B3%29%5E2+=+%284sqrt%28x-2%29%29%5E2+
+x%5E2%2B6x%2B9+=+16%28x-2%29+
+x%5E2%2B6x%2B9+=+16x-32+
+x%5E2-10x%2B41+=+0+

Put this into the quadratic formula and you get 5+%2B-+4i+ as the answer - if you have done the topic "Complex numbers". If not, then your answer is "there is no answer" :-)

jon.