Solve x^2+2=33

$${ x }^{ 2 } +2=33$$

Solve for x

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

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

Steps by Finding Square Root

Subtract 2 from both sides.

$$x^{2}=33-2$$

Subtract 2 from 33 to get 31.

$$x^{2}=31$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 33 from both sides.

$$x^{2}+2-33=0$$

Subtract 33 from 2 to get -31.

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

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.

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