SOLUTION: simplify -√x^2+4x+4

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Question 271416: simplify
-√x^2+4x+4

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If your problem is not
-sqrt%28x%5E2%2B4x%2B4%29
then please repost your question and use parentheses around the expression that belongs inside the square root and use parentheses around the expression to which the "-" applies.

To simplify this expression, we need to recognize that x%5E2%2B4x%2B4 fits the pattern a%5E2+%2B2ab+%2B+b%5E2+=+%28a%2Bb%29%5E2 with a = x and b = 2. So our expression can be rewritten as:
-sqrt%28%28x%2B2%29%5E2%29
Now we have the square root of a perfect square! The easy mistake to make here is to think that sqrt%28%28x%2B2%29%5E2%29+=+x%2B2. But a square root is supposed to positive. And x+2 may not be positive. So we use absolute value to ensure a positive square root:
-abs%28x%2B2%29