Solve 2(1+x)^2=24

$$2 ( 1 + x ) ^ { 2 } = 24$$

Solve for x

$$x=2\sqrt{3}-1\approx 2.464101615$$

$$x=-2\sqrt{3}-1\approx -4.464101615$$

Steps by Finding Square Root

Divide both sides by 2.

$$\frac{2\left(x+1\right)^{2}}{2}=\frac{24}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\left(x+1\right)^{2}=\frac{24}{2}$$

Divide 24 by 2.

$$\left(x+1\right)^{2}=12$$

Take the square root of both sides of the equation.

$$x+1=2\sqrt{3} x+1=-2\sqrt{3}$$

Subtract 1 from both sides of the equation.

$$x+1-1=2\sqrt{3}-1 x+1-1=-2\sqrt{3}-1$$

Subtracting 1 from itself leaves 0.

$$x=2\sqrt{3}-1 x=-2\sqrt{3}-1$$