Solve 57.5(1-x)^2=82.2

$$57.5 ( 1 - x ) ^ { 2 } = 82.2$$

Solve for x

$$x=-\frac{\sqrt{18906}}{115}+1\approx -0.195644269$$

$$x=\frac{\sqrt{18906}}{115}+1\approx 2.195644269$$

Steps by Finding Square Root

Divide both sides of the equation by 57.5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{57.5\left(-x+1\right)^{2}}{57.5}=\frac{82.2}{57.5}$$

Dividing by 57.5 undoes the multiplication by 57.5.

$$\left(-x+1\right)^{2}=\frac{82.2}{57.5}$$

Divide 82.2 by 57.5 by multiplying 82.2 by the reciprocal of 57.5.

$$\left(-x+1\right)^{2}=\frac{822}{575}$$

Take the square root of both sides of the equation.

$$-x+1=\frac{\sqrt{18906}}{115} -x+1=-\frac{\sqrt{18906}}{115}$$

Subtract 1 from both sides of the equation.

$$-x+1-1=\frac{\sqrt{18906}}{115}-1 -x+1-1=-\frac{\sqrt{18906}}{115}-1$$

Subtracting 1 from itself leaves 0.

$$-x=\frac{\sqrt{18906}}{115}-1 -x=-\frac{\sqrt{18906}}{115}-1$$

Subtract 1 from \frac{\sqrt{18906}}{115}.

$$-x=\frac{\sqrt{18906}}{115}-1$$

Subtract 1 from -\frac{\sqrt{18906}}{115}.

$$-x=-\frac{\sqrt{18906}}{115}-1$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\frac{\sqrt{18906}}{115}-1}{-1} \frac{-x}{-1}=\frac{-\frac{\sqrt{18906}}{115}-1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\frac{\sqrt{18906}}{115}-1}{-1} x=\frac{-\frac{\sqrt{18906}}{115}-1}{-1}$$

Divide \frac{\sqrt{18906}}{115}-1 by -1.

$$x=-\frac{\sqrt{18906}}{115}+1$$

Divide -\frac{\sqrt{18906}}{115}-1 by -1.

$$x=\frac{\sqrt{18906}}{115}+1$$

The equation is now solved.

$$x=-\frac{\sqrt{18906}}{115}+1 x=\frac{\sqrt{18906}}{115}+1$$