SOLUTION: squareroot x + squareroot x-5 = 5 Solve equation & check for extraneous solutions

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Question 184673This question is from textbook
: squareroot x + squareroot x-5 = 5

Solve equation & check for extraneous solutions This question is from textbook

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28x%29+%2B+sqrt%28x-5%29+=+5 

Solve equation & check for extraneous solutions

sqrt%28x%29+%2B+sqrt%28x-5%29+=+5 

Isolate the more complicated radical:

sqrt%28x-5%29+=+5+-+sqrt%28x%29

Square both sides

%28sqrt%28x-5%29%29%5E2+=+%285+-+sqrt%28x%29%29%5E2

The left side is just x-5 because it just
has one term in the parentheses. But the right 
side has two terms, so to square it you must
write it down twice and multiply it by itself:

x-5+=+%285+-+sqrt%28x%29%29%285-sqrt%28x%29%29

Use FOIL on the right:

x-5+=+25+-+5sqrt%28x%29-5sqrt%28x%29%2B%28sqrt%28x%29%29%5E2+

x-5+=+25+-+10sqrt%28x%29%2Bx+

Simplify the equation

10sqrt%28x%29=30

Divide through by 10 

sqrt%28x%29=3

Square both sides:

%28sqrt%28x%29%29%5E2+=+3%5E2

x=9

Check:

sqrt%28x%29+%2B+sqrt%28x-5%29+=+5
sqrt%289%29+%2B+sqrt%289-5%29+=+5
sqrt%289%29+%2B+sqrt%284%29+=+5
3%2B2=5
5=5

So the solution is 9

Edwin