Solve 20.55*(1+x)^2=23.82

$$20.55 \times ( 1 + x ) ^ { 2 } = 23.82$$

Solve for x

$$x=\frac{\sqrt{543890}}{685}-1\approx 0.076626253$$

$$x=-\frac{\sqrt{543890}}{685}-1\approx -2.076626253$$

Steps by Finding Square Root

Divide both sides of the equation by 20.55, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{20.55\left(x+1\right)^{2}}{20.55}=\frac{23.82}{20.55}$$

Dividing by 20.55 undoes the multiplication by 20.55.

$$\left(x+1\right)^{2}=\frac{23.82}{20.55}$$

Divide 23.82 by 20.55 by multiplying 23.82 by the reciprocal of 20.55.

$$\left(x+1\right)^{2}=\frac{794}{685}$$

Take the square root of both sides of the equation.

$$x+1=\frac{\sqrt{543890}}{685} x+1=-\frac{\sqrt{543890}}{685}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{\sqrt{543890}}{685}-1 x+1-1=-\frac{\sqrt{543890}}{685}-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{\sqrt{543890}}{685}-1 x=-\frac{\sqrt{543890}}{685}-1$$