Solve 225(1-x)^2=64

$$225 ( 1 - x ) ^ { 2 } = 64$$

Solve for x

$$x=\frac{7}{15}\approx 0.466666667$$

$$x = \frac{23}{15} = 1\frac{8}{15} \approx 1.533333333$$

Steps by Finding Square Root

Divide both sides by 225.

$$\frac{225\left(-x+1\right)^{2}}{225}=\frac{64}{225}$$

Dividing by 225 undoes the multiplication by 225.

$$\left(-x+1\right)^{2}=\frac{64}{225}$$

Take the square root of both sides of the equation.

$$-x+1=\frac{8}{15} -x+1=-\frac{8}{15}$$

Subtract 1 from both sides of the equation.

$$-x+1-1=\frac{8}{15}-1 -x+1-1=-\frac{8}{15}-1$$

Subtracting 1 from itself leaves 0.

$$-x=\frac{8}{15}-1 -x=-\frac{8}{15}-1$$

Subtract 1 from \frac{8}{15}.

$$-x=-\frac{7}{15}$$

Subtract 1 from -\frac{8}{15}.

$$-x=-\frac{23}{15}$$

Divide both sides by -1.

$$\frac{-x}{-1}=-\frac{\frac{7}{15}}{-1} \frac{-x}{-1}=-\frac{\frac{23}{15}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=-\frac{\frac{7}{15}}{-1} x=-\frac{\frac{23}{15}}{-1}$$

Divide -\frac{7}{15} by -1.

$$x=\frac{7}{15}$$

Divide -\frac{23}{15} by -1.

$$x=\frac{23}{15}$$

The equation is now solved.

$$x=\frac{7}{15} x=\frac{23}{15}$$