Solve 100*left(x-1right)^2=8

$$100 \times { \left(x-1 \right) }^{ 2 } =8$$

Solve for x

$$x=\frac{\sqrt{2}}{5}+1\approx 1.282842712$$

$$x=-\frac{\sqrt{2}}{5}+1\approx 0.717157288$$

Steps by Finding Square Root

Divide both sides by 100.

$$\frac{100\left(x-1\right)^{2}}{100}=\frac{8}{100}$$

Dividing by 100 undoes the multiplication by 100.

$$\left(x-1\right)^{2}=\frac{8}{100}$$

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

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

Take the square root of both sides of the equation.

$$x-1=\frac{\sqrt{2}}{5} x-1=-\frac{\sqrt{2}}{5}$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=\frac{\sqrt{2}}{5}-\left(-1\right) x-1-\left(-1\right)=-\frac{\sqrt{2}}{5}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=\frac{\sqrt{2}}{5}-\left(-1\right) x=-\frac{\sqrt{2}}{5}-\left(-1\right)$$

Subtract -1 from \frac{\sqrt{2}}{5}.

$$x=\frac{\sqrt{2}}{5}+1$$

Subtract -1 from -\frac{\sqrt{2}}{5}.

$$x=-\frac{\sqrt{2}}{5}+1$$

The equation is now solved.

$$x=\frac{\sqrt{2}}{5}+1 x=-\frac{\sqrt{2}}{5}+1$$