Solve N^2-3=21

$$N ^ { 2 } - 3 = 21$$

Solve for N

$$N=2\sqrt{6}\approx 4.898979486$$

$$N=-2\sqrt{6}\approx -4.898979486$$

Steps by Finding Square Root

Add 3 to both sides.

$$N^{2}=21+3$$

Add 21 and 3 to get 24.

$$N^{2}=24$$

Take the square root of both sides of the equation.

$$N=2\sqrt{6} N=-2\sqrt{6}$$

Steps Using the Quadratic Formula

Subtract 21 from both sides.

$$N^{2}-3-21=0$$

Subtract 21 from -3 to get -24.

$$N^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$N=\frac{0±\sqrt{0^{2}-4\left(-24\right)}}{2}$$

Square 0.

$$N=\frac{0±\sqrt{-4\left(-24\right)}}{2}$$

Multiply -4 times -24.

$$N=\frac{0±\sqrt{96}}{2}$$

Take the square root of 96.

$$N=\frac{0±4\sqrt{6}}{2}$$

Now solve the equation N=\frac{0±4\sqrt{6}}{2} when ± is plus.

$$N=2\sqrt{6}$$

Now solve the equation N=\frac{0±4\sqrt{6}}{2} when ± is minus.

$$N=-2\sqrt{6}$$

The equation is now solved.

$$N=2\sqrt{6} N=-2\sqrt{6}$$