Solve (2x+3)^2=11

$$( 2 x + 3 ) ^ { 2 } = 11$$

Solve for x

$$x=\frac{\sqrt{11}-3}{2}\approx 0.158312395$$

$$x=\frac{-\sqrt{11}-3}{2}\approx -3.158312395$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$2x+3=\sqrt{11} 2x+3=-\sqrt{11}$$

Subtract 3 from both sides of the equation.

$$2x+3-3=\sqrt{11}-3 2x+3-3=-\sqrt{11}-3$$

Subtracting 3 from itself leaves 0.

$$2x=\sqrt{11}-3 2x=-\sqrt{11}-3$$

Subtract 3 from \sqrt{11}.

$$2x=\sqrt{11}-3$$

Subtract 3 from -\sqrt{11}.

$$2x=-\sqrt{11}-3$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{\sqrt{11}-3}{2} \frac{2x}{2}=\frac{-\sqrt{11}-3}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{\sqrt{11}-3}{2} x=\frac{-\sqrt{11}-3}{2}$$