Solve 400(1-x)^2=256

$$400 ( 1 - x ) ^ { 2 } = 256$$

Solve for x

$$x=\frac{1}{5}=0.2$$

$$x = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

Steps by Finding Square Root

Divide both sides by 400.

$$\frac{400\left(-x+1\right)^{2}}{400}=\frac{256}{400}$$

Dividing by 400 undoes the multiplication by 400.

$$\left(-x+1\right)^{2}=\frac{256}{400}$$

Reduce the fraction \frac{256}{400} to lowest terms by extracting and canceling out 16.

$$\left(-x+1\right)^{2}=\frac{16}{25}$$

Take the square root of both sides of the equation.

$$-x+1=\frac{4}{5} -x+1=-\frac{4}{5}$$

Subtract 1 from both sides of the equation.

$$-x+1-1=\frac{4}{5}-1 -x+1-1=-\frac{4}{5}-1$$

Subtracting 1 from itself leaves 0.

$$-x=\frac{4}{5}-1 -x=-\frac{4}{5}-1$$

Subtract 1 from \frac{4}{5}.

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

Subtract 1 from -\frac{4}{5}.

$$-x=-\frac{9}{5}$$

Divide both sides by -1.

$$\frac{-x}{-1}=-\frac{\frac{1}{5}}{-1} \frac{-x}{-1}=-\frac{\frac{9}{5}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=-\frac{\frac{1}{5}}{-1} x=-\frac{\frac{9}{5}}{-1}$$

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

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

Divide -\frac{9}{5} by -1.

$$x=\frac{9}{5}$$

The equation is now solved.

$$x=\frac{1}{5} x=\frac{9}{5}$$