Solve 4(x-1)^2=48

$$4 ( x - 1 ) ^ { 2 } = 48$$

Solve for x

$$x=2\sqrt{3}+1\approx 4.464101615$$

$$x=1-2\sqrt{3}\approx -2.464101615$$

Steps by Finding Square Root

Divide both sides by 4.

$$\frac{4\left(x-1\right)^{2}}{4}=\frac{48}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\left(x-1\right)^{2}=\frac{48}{4}$$

Divide 48 by 4.

$$\left(x-1\right)^{2}=12$$

Take the square root of both sides of the equation.

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

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=2\sqrt{3}-\left(-1\right) x-1-\left(-1\right)=-2\sqrt{3}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=2\sqrt{3}-\left(-1\right) x=-2\sqrt{3}-\left(-1\right)$$

Subtract -1 from 2\sqrt{3}.

$$x=2\sqrt{3}+1$$

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

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

The equation is now solved.

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