SOLUTION: Solve algebraically and check your potential solutions: √x+2-x=0

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Question 196588: Solve algebraically and check your potential solutions: √x+2-x=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B2%29-x=0 Start with the given equation.


sqrt%28x%2B2%29=x Add "x" to both sides.


x%2B2=x%5E2 Square both sides.


0=x%5E2-x-2 Get all terms to one side.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=1, B=-1, and C=-2


Let's use the quadratic formula to solve for x


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-1, and C=-2


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--8+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-2%29 to get -8


x+=+%281+%2B-+sqrt%28+1%2B8+%29%29%2F%282%281%29%29 Rewrite sqrt%281--8%29 as sqrt%281%2B8%29


x+=+%281+%2B-+sqrt%28+9+%29%29%2F%282%281%29%29 Add 1 to 8 to get 9


x+=+%281+%2B-+sqrt%28+9+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+3%29%2F%282%29 Take the square root of 9 to get 3.


x+=+%281+%2B+3%29%2F%282%29 or x+=+%281+-+3%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29 or x+=++%28-2%29%2F%282%29 Combine like terms.


x+=+2 or x+=+-1 Simplify.


So the answers are x+=+2 or x+=+-1

However, if we plug in x+=+-1, we'll find that a contradiction will result.


So the only solution is x+=+2