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How do you solve #|x^2+2x|=0#?

Answer 1

Savannah Anderson

Simply removing the absolute value.

The absolute value can be solved considering two equations, one with the plus and one with the minus.

#|x^2+2x|=0#

#+(x^2+2x)=0#

#-(x^2+2x)=0#

In this case both equations are identical because you can multiply for #-1# left and right the equations transforming one in the other.

Then the solution is

#x^2+2x=0#

#x(x+2)=0# that has two solutions, one that is #x=0# and the other #x=-2#.

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Answer 2

Eva Adamson

To solve the equation |x^2 + 2x| = 0, you set the expression inside the absolute value bars equal to zero and solve for x.

So, x^2 + 2x = 0.

Factoring out x from the expression, you get:

x(x + 2) = 0.

Setting each factor equal to zero, you find the solutions for x:

x = 0 or x + 2 = 0.

Solving for x in the second equation, you get:

x = -2.

Therefore, the solutions to the equation |x^2 + 2x| = 0 are x = 0 and x = -2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.