Solve for: x ^ 2-3 = 0

Expression: $$x ^ { 2 } - 3 = 0$$

Quadratic equations like this one, with an $x^{2}$ term but no $x$ term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$, once they are put in standard form: $ax^{2}+bx+c=0$.

$$x^{2}-3=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-3$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-3\right)}}{2}$$

Multiply $-4$ times $-3$.

$$x=\frac{0±\sqrt{12}}{2}$$

Take the square root of $12$.

$$x=\frac{0±2\sqrt{3}}{2}$$

Now solve the equation $x=\frac{0±2\sqrt{3}}{2}$ when $±$ is plus.

$$x=\sqrt{3}$$

Now solve the equation $x=\frac{0±2\sqrt{3}}{2}$ when $±$ is minus.

$$x=-\sqrt{3}$$

The equation is now solved.

$$x=\sqrt{3}$$ $$x=-\sqrt{3}$$