SOLUTION: Explain why there are no real numbers that satisfy the equation |x^2 + 4x| =

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Question 1207832: Explain why there are no real numbers that satisfy the equation |x^2 + 4x| = - 12.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
The absolute value is only zero or greater. Absolute value cannot have a negative number value as the given equation is expressing.

Answer by ikleyn(52814)   (Show Source):
You can put this solution on YOUR website!
.

By the definition, absolute value of a number or of an expression is always positive real number or zero.

Therefore, left side of this equality can not be equal to negative number in right side.

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Comment from student: You are saying this: |blah| must = positive number

My response:   Not exactly. I said something different. I said

        "absolute value of a number or of an expression is always positive real number or zero".

Please do not distort my words.

I just got several comments from you in response to my solutions.

These comments had something in common: every time you try to distort my words.

Distorting my words, you distort their meaning.

I am VERY DISAPPOINTED to see it again and again. Please do not make it in the future.

Don't make me justify myself by twisting my words.

SOLUTION: Explain why there are no real numbers that satisfy the equation |x^2 + 4x| = - 12.