Solve 0.08(1+x)^2=0.16

$$0.08 ( 1 + x ) ^ { 2 } = 0.16$$

Solve for x

$$x=\sqrt{2}-1\approx 0.414213562$$

$$x=-\left(\sqrt{2}+1\right)\approx -2.414213562$$

Steps by Finding Square Root

Divide both sides of the equation by 0.08, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.08\left(x+1\right)^{2}}{0.08}=\frac{0.16}{0.08}$$

Dividing by 0.08 undoes the multiplication by 0.08.

$$\left(x+1\right)^{2}=\frac{0.16}{0.08}$$

Divide 0.16 by 0.08 by multiplying 0.16 by the reciprocal of 0.08.

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

Take the square root of both sides of the equation.

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

Subtract 1 from both sides of the equation.

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

Subtracting 1 from itself leaves 0.

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