Solve (x-1)^2-5=0

$$( x - 1 ) ^ { 2 } - 5 = 0$$

Solve for x

$$x=\sqrt{5}+1\approx 3.236067977$$

$$x=1-\sqrt{5}\approx -1.236067977$$

Steps by Finding Square Root

Add 5 to both sides of the equation.

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

Subtracting 5 from itself leaves 0.

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

Take the square root of both sides of the equation.

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

Add 1 to both sides of the equation.

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

Subtracting -1 from itself leaves 0.

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

Subtract -1 from \sqrt{5}.

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

Subtract -1 from -\sqrt{5}.

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

The equation is now solved.

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