Solve 4^2=x^2+2

$$4 ^ { 2 } = x ^ { 2 } + 2$$

Solve for x

$$x=\sqrt{14}\approx 3.741657387$$

$$x=-\sqrt{14}\approx -3.741657387$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

$$16=x^{2}+2$$

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

$$x^{2}+2=16$$

Subtract 2 from both sides.

$$x^{2}=16-2$$

Subtract 2 from 16 to get 14.

$$x^{2}=14$$

Take the square root of both sides of the equation.

$$x=\sqrt{14} x=-\sqrt{14}$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

$$16=x^{2}+2$$

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

$$x^{2}+2=16$$

Subtract 16 from both sides.

$$x^{2}+2-16=0$$

Subtract 16 from 2 to get -14.

$$x^{2}-14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-14\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-14\right)}}{2}$$

Multiply -4 times -14.

$$x=\frac{0±\sqrt{56}}{2}$$

Take the square root of 56.

$$x=\frac{0±2\sqrt{14}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{14}}{2} when ± is plus.

$$x=\sqrt{14}$$

Now solve the equation x=\frac{0±2\sqrt{14}}{2} when ± is minus.

$$x=-\sqrt{14}$$

The equation is now solved.

$$x=\sqrt{14} x=-\sqrt{14}$$