Solve 0=x^2-42

$$0 = x ^ { 2 } - 42$$

Solve for x

$$x=\sqrt{42}\approx 6.480740698$$

$$x=-\sqrt{42}\approx -6.480740698$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-42=0$$

Add 42 to both sides. Anything plus zero gives itself.

$$x^{2}=42$$

Take the square root of both sides of the equation.

$$x=\sqrt{42} x=-\sqrt{42}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-42=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -42 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-42\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-42\right)}}{2}$$

Multiply -4 times -42.

$$x=\frac{0±\sqrt{168}}{2}$$

Take the square root of 168.

$$x=\frac{0±2\sqrt{42}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{42}}{2} when ± is plus.

$$x=\sqrt{42}$$

Now solve the equation x=\frac{0±2\sqrt{42}}{2} when ± is minus.

$$x=-\sqrt{42}$$

The equation is now solved.

$$x=\sqrt{42} x=-\sqrt{42}$$