Solve (2n+1)^2=20

$$( 2 n + 1 ) ^ { 2 } = 20$$

Solve for n

$$n=\sqrt{5}-\frac{1}{2}\approx 1.736067977$$

$$n=-\sqrt{5}-\frac{1}{2}\approx -2.736067977$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$2n+1=2\sqrt{5} 2n+1=-2\sqrt{5}$$

Subtract 1 from both sides of the equation.

$$2n+1-1=2\sqrt{5}-1 2n+1-1=-2\sqrt{5}-1$$

Subtracting 1 from itself leaves 0.

$$2n=2\sqrt{5}-1 2n=-2\sqrt{5}-1$$

Subtract 1 from 2\sqrt{5}.

$$2n=2\sqrt{5}-1$$

Subtract 1 from -2\sqrt{5}.

$$2n=-2\sqrt{5}-1$$

Divide both sides by 2.

$$\frac{2n}{2}=\frac{2\sqrt{5}-1}{2} \frac{2n}{2}=\frac{-2\sqrt{5}-1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$n=\frac{2\sqrt{5}-1}{2} n=\frac{-2\sqrt{5}-1}{2}$$

Divide 2\sqrt{5}-1 by 2.

$$n=\sqrt{5}-\frac{1}{2}$$

Divide -2\sqrt{5}-1 by 2.

$$n=-\sqrt{5}-\frac{1}{2}$$

The equation is now solved.

$$n=\sqrt{5}-\frac{1}{2} n=-\sqrt{5}-\frac{1}{2}$$