why is the solution to $x^2 = 3$ the same as $x = \pm \sqrt 3$

Question

I understand that in order to simplify $x$ in this equation: $x^2 = 3$ we would need to get the square root on both sides what i dont understand is the fact that it is written as $x = \pm \sqrt 3$. I don't understand where the $±$ comes from , this problem was a part of solving polynomials by factoring and I just want the reasoning behind why it wouldn't simply be $x = \sqrt 3$ but $x = x = \pm \sqrt 3$.

the original equation : $2x^5+12x^3 -54x = 0$

my solutions :

$x=0 $
$x=\pm \sqrt 3$
$x = \pm 3i$

Answer 1

That's because you can square either $-\sqrt3$ or $\sqrt3$ to get $3$ and the question requires you to find a real/complex number that can be squared to give $3$ as the answer.

Answer 2

We are looking for $x$ such that

$$x^2 = 3$$

and since both $x=\sqrt 3$ and $x=-\sqrt 3$ satisfy the equation, these are the two roots for the given equation.

Answer 3

It comes from the identity $\sqrt{x^2}=|x|$. Now, solve $|x|=\sqrt{3}$.
Also, $x^2=3$; $x^2-3=0$; $(x-\sqrt{3})(x+\sqrt{3})=0$