SOLUTION: please solve the equation. directions i was given: solve the following. {{{ x=(Square root)x+2 }}} thank you

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Question 174721: please solve the equation.
directions i was given:
solve the following.
+x=%28Square+root%29x%2B2+
thank you
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the equation x=sqrt%28x%29%2B2 ???


x=sqrt%28x%29%2B2 Start with the given equation.


x-2=sqrt%28x%29 Subtract 2 from both sides.


%28x-2%29%5E2=x Square both sides.


x%5E2-4x%2B4=x FOIL.


x%5E2-4x%2B4-x=0 Subtract x from both sides.


x%5E2-5x%2B4=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-5, and c=4


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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-5, and c=4


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%281%29%284%29+%29%29%2F%282%281%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25-16+%29%29%2F%282%281%29%29 Multiply 4%281%29%284%29 to get 16


x+=+%285+%2B-+sqrt%28+9+%29%29%2F%282%281%29%29 Subtract 16 from 25 to get 9


x+=+%285+%2B-+sqrt%28+9+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%285+%2B-+3%29%2F%282%29 Take the square root of 9 to get 3.


x+=+%285+%2B+3%29%2F%282%29 or x+=+%285+-+3%29%2F%282%29 Break up the expression.


x+=+%288%29%2F%282%29 or x+=++%282%29%2F%282%29 Combine like terms.


x+=+4 or x+=+1 Simplify.


Take note that if we plug in x+=+1, we get an inconsistent equation. So x+=+1 is NOT a solution




So the answer is x+=+4


Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
x=sqrt%28x%29%2B2
:
x-2=sqrt%28x%29isolating the radical
:
%28x-2%29%5E2=%28sqrt%28x%29%29%5E2squaring both sides
:
x%5E2-4x%2B4=xmultiplying terms
:
x%5E2-5x%2B4=0combining like terms
:
%28x-4%29%28x-1%29=0factoring
:
x=4 and 1
because we squared these terms we must check for extraneous roots.
:
upon checking 1 is thrown out
:
and the final solution is highlight%28x=4%29