Solve 193=x^2

$$193= { x }^{ 2 }$$

Solve for x

$$x=\sqrt{193}\approx 13.892443989$$

$$x=-\sqrt{193}\approx -13.892443989$$

Steps by Finding Square Root

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

$$x^{2}=193$$

Take the square root of both sides of the equation.

$$x=\sqrt{193} x=-\sqrt{193}$$

Steps Using the Quadratic Formula

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

$$x^{2}=193$$

Subtract 193 from both sides.

$$x^{2}-193=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -193 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-193\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-193\right)}}{2}$$

Multiply -4 times -193.

$$x=\frac{0±\sqrt{772}}{2}$$

Take the square root of 772.

$$x=\frac{0±2\sqrt{193}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{193}}{2} when ± is plus.

$$x=\sqrt{193}$$

Now solve the equation x=\frac{0±2\sqrt{193}}{2} when ± is minus.

$$x=-\sqrt{193}$$

The equation is now solved.

$$x=\sqrt{193} x=-\sqrt{193}$$