Solve n^2-2=26

$$n ^ { 2 } - 2 = 26$$

Solve for n

$$n=2\sqrt{7}\approx 5.291502622$$

$$n=-2\sqrt{7}\approx -5.291502622$$

Steps by Finding Square Root

Add 2 to both sides.

$$n^{2}=26+2$$

Add 26 and 2 to get 28.

$$n^{2}=28$$

Take the square root of both sides of the equation.

$$n=2\sqrt{7} n=-2\sqrt{7}$$

Steps Using the Quadratic Formula

Subtract 26 from both sides.

$$n^{2}-2-26=0$$

Subtract 26 from -2 to get -28.

$$n^{2}-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-28\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-28\right)}}{2}$$

Multiply -4 times -28.

$$n=\frac{0±\sqrt{112}}{2}$$

Take the square root of 112.

$$n=\frac{0±4\sqrt{7}}{2}$$

Now solve the equation n=\frac{0±4\sqrt{7}}{2} when ± is plus.

$$n=2\sqrt{7}$$

Now solve the equation n=\frac{0±4\sqrt{7}}{2} when ± is minus.

$$n=-2\sqrt{7}$$

The equation is now solved.

$$n=2\sqrt{7} n=-2\sqrt{7}$$