Solve 25(x-1)^2=16

$$25 ( x - 1 ) ^ { 2 } = 16$$

Solve for x

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

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

Steps by Finding Square Root

Divide both sides by 25.

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

Dividing by 25 undoes the multiplication by 25.

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

Take the square root of both sides of the equation.

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

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=\frac{4}{5}-\left(-1\right) x-1-\left(-1\right)=-\frac{4}{5}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=\frac{4}{5}-\left(-1\right) x=-\frac{4}{5}-\left(-1\right)$$

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

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

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

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

The equation is now solved.

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