Solve 4(x-1)^2=1

$$4 ( x - 1 ) ^ { 2 } = 1$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$x=\frac{1}{2}=0.5$$

Steps by Finding Square Root

Divide both sides by 4.

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

Dividing by 4 undoes the multiplication by 4.

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

Take the square root of both sides of the equation.

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

Add 1 to both sides of the equation.

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

Subtracting -1 from itself leaves 0.

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

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

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

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

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

The equation is now solved.

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