Solve x^2=338

$${ x }^{ 2 } =338$$

Solve for x

$$x=13\sqrt{2}\approx 18.384776311$$

$$x=-13\sqrt{2}\approx -18.384776311$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=13\sqrt{2} x=-13\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract 338 from both sides.

$$x^{2}-338=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -338 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-338\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-338\right)}}{2}$$

Multiply -4 times -338.

$$x=\frac{0±\sqrt{1352}}{2}$$

Take the square root of 1352.

$$x=\frac{0±26\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±26\sqrt{2}}{2} when ± is plus.

$$x=13\sqrt{2}$$

Now solve the equation x=\frac{0±26\sqrt{2}}{2} when ± is minus.

$$x=-13\sqrt{2}$$

The equation is now solved.

$$x=13\sqrt{2} x=-13\sqrt{2}$$