Solve 90(1-x)^2=40

$$90 ( 1 - x ) ^ { 2 } = 40$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps by Finding Square Root

Divide both sides by 90.

$$\frac{90\left(-x+1\right)^{2}}{90}=\frac{40}{90}$$

Dividing by 90 undoes the multiplication by 90.

$$\left(-x+1\right)^{2}=\frac{40}{90}$$

Reduce the fraction \frac{40}{90} to lowest terms by extracting and canceling out 10.

$$\left(-x+1\right)^{2}=\frac{4}{9}$$

Take the square root of both sides of the equation.

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

Subtract 1 from both sides of the equation.

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

Subtracting 1 from itself leaves 0.

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

Subtract 1 from \frac{2}{3}.

$$-x=-\frac{1}{3}$$

Subtract 1 from -\frac{2}{3}.

$$-x=-\frac{5}{3}$$

Divide both sides by -1.

$$\frac{-x}{-1}=-\frac{\frac{1}{3}}{-1} \frac{-x}{-1}=-\frac{\frac{5}{3}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=-\frac{\frac{1}{3}}{-1} x=-\frac{\frac{5}{3}}{-1}$$

Divide -\frac{1}{3} by -1.

$$x=\frac{1}{3}$$

Divide -\frac{5}{3} by -1.

$$x=\frac{5}{3}$$

The equation is now solved.

$$x=\frac{1}{3} x=\frac{5}{3}$$