How do you solve $∣ ∣ x^{2} + 2 x ∣ ∣ = 0$ $|x^2+2x|=0$ ?

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Answer 1 · 2016-06-17T19:11:06

Simply removing the absolute value.

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

$∣ ∣ x^{2} + 2 x ∣ ∣ = 0$ $|x^2+2x|=0$

$+ (x^{2} + 2 x) = 0$ $+(x^2+2x)=0$

$- (x^{2} + 2 x) = 0$ $-(x^2+2x)=0$

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

Then the solution is

$x^{2} + 2 x = 0$ $x^2+2x=0$

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

How do you solve ∣∣x2+2x∣∣=0|x^2+2x|=0?