Solve 5(x-1)^2=15

$$5 ( x - 1 ) ^ { 2 } = 15$$

Solve for x

$$x=\sqrt{3}+1\approx 2.732050808$$

$$x=1-\sqrt{3}\approx -0.732050808$$

Steps by Finding Square Root

Divide both sides by 5.

$$\frac{5\left(x-1\right)^{2}}{5}=\frac{15}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$\left(x-1\right)^{2}=\frac{15}{5}$$

Divide 15 by 5.

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

Take the square root of both sides of the equation.

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

Add 1 to both sides of the equation.

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

Subtracting -1 from itself leaves 0.

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

Subtract -1 from \sqrt{3}.

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

Subtract -1 from -\sqrt{3}.

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

The equation is now solved.

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