Some misunderstanding on quadratic equation.

Question

I have the following equation

$$x^2+4x+4=0$$

When I calculate $x = -2$. So I can write equation as follows

$$(x-2)^2=0$$

But when I open parenthesis, this $x^2-4x+4$ is not equal to this $x^2+4x+4$.

Any idea what do I miss here why two equations not equal?

Answer 1

To be more specific, it's supposed to be $(x-(-2))^2$. Try to substitute $x=-2$ into that expression and see what you get. That should help you understand why the signs are the way they are.

Answer 2

That's because $x^2 +4x +4$ is not equal to $(x-2)^2$, but rather $(x+2)^2$.

This makes your equation $$(x+2)^2 =0$$

The solutions are $x=-2,-2$