Solve left(2x+1right)^2=116

$${ \left(2x+1 \right) }^{ 2 } =116$$

Solve for x

$$x=\sqrt{29}-\frac{1}{2}\approx 4.885164807$$

$$x=-\sqrt{29}-\frac{1}{2}\approx -5.885164807$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$2x+1=2\sqrt{29} 2x+1=-2\sqrt{29}$$

Subtract 1 from both sides of the equation.

$$2x+1-1=2\sqrt{29}-1 2x+1-1=-2\sqrt{29}-1$$

Subtracting 1 from itself leaves 0.

$$2x=2\sqrt{29}-1 2x=-2\sqrt{29}-1$$

Subtract 1 from 2\sqrt{29}.

$$2x=2\sqrt{29}-1$$

Subtract 1 from -2\sqrt{29}.

$$2x=-2\sqrt{29}-1$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{2\sqrt{29}-1}{2} \frac{2x}{2}=\frac{-2\sqrt{29}-1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{2\sqrt{29}-1}{2} x=\frac{-2\sqrt{29}-1}{2}$$

Divide 2\sqrt{29}-1 by 2.

$$x=\sqrt{29}-\frac{1}{2}$$

Divide -2\sqrt{29}-1 by 2.

$$x=-\sqrt{29}-\frac{1}{2}$$

The equation is now solved.

$$x=\sqrt{29}-\frac{1}{2} x=-\sqrt{29}-\frac{1}{2}$$