SOLUTION: solve for x sqrt x+7+5= x

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Question 114778: solve for x
sqrt x+7+5= x
Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to assume you mean sqrt%28x%2B7%29%2B5=x.

1) Add -5 to both sides
sqrt%28x%2B7%29=x-5

2) Square both sides
x%2B7=x%5E2-10x%2B25

3) Collect terms and put in standard form
x%5E2-11x%2B18=0

4) Factor
-9%2A-2=18
-9%2B%28-2%29=-11
%28x-9%29%28x-2%29=0
x=9 or x=2

Check:
sqrt%289%2B7%29%2B5=9
sqrt%2816%29%2B5=9
4%2B5=9 Check
sqrt%282%2B7%29%2B5=2
sqrt%289%29%2B5=2
3%2B5%3C%3E2 Does not check. Why? By squaring both sides of the equation in step 2), you introduced an extraneous root that is invalid in the original equation. Therefore exclude x=2 from the solution set. The only correct solution is x=9

Graphically:
graph%28400%2C+400%2C+-8%2C+25%2C+-10%2C+14%2C+sqrt%28x%2B7%29%2B5-x%29