Why is it true that $∀x((-x)^2=x^2)$?

I'm trying to learn discrete math and I'm lost as to why this truth value is true. Can anyone please explain why? The domain consists of all real numbers.

$∀x((-x)^2=x^2)$

The answer is True, but I can't see why that's so.

I'm reading this as for the set of all real numbers, $-x^2=x^2$, which if I just choose a random number, like say 1, I get -1=1. What's up with this? Am I way missing something?

Thanks.

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It says that $(-x)^2=x^2$. Note the parentheses: $(-x)^2$ is the square of $-x$. So $(-1)^2=1$. – André Nicolas Jan 12 '13 at 5:01
wow, duh. my brain is friend from too much math today. i was trying to prove this to myself with a calculator and was using the x^2 button, but of course, was using it incorrectly. – user56763 Jan 12 '13 at 5:05
Please try to use more descriptive titles. – Rahul Jan 12 '13 at 6:06

$$(-x)^2 = (-x)\cdot(-x) = (-1)\cdot(-1)\cdot x^2=x^2$$ Hence for $x=1$
$$(-1)^2 = (-1)\cdot(-1) = (-1)\cdot(-1)=1^2=1$$