Solve X^2=31

$$X ^ { 2 } = 31$$

Solve for X

$$X=\sqrt{31}\approx 5.567764363$$

$$X=-\sqrt{31}\approx -5.567764363$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$X=\sqrt{31} X=-\sqrt{31}$$

Steps Using the Quadratic Formula

Subtract 31 from both sides.

$$X^{2}-31=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -31 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$X=\frac{0±\sqrt{0^{2}-4\left(-31\right)}}{2}$$

Square 0.

$$X=\frac{0±\sqrt{-4\left(-31\right)}}{2}$$

Multiply -4 times -31.

$$X=\frac{0±\sqrt{124}}{2}$$

Take the square root of 124.

$$X=\frac{0±2\sqrt{31}}{2}$$

Now solve the equation X=\frac{0±2\sqrt{31}}{2} when ± is plus.

$$X=\sqrt{31}$$

Now solve the equation X=\frac{0±2\sqrt{31}}{2} when ± is minus.

$$X=-\sqrt{31}$$

The equation is now solved.

$$X=\sqrt{31} X=-\sqrt{31}$$