Solve left(1-xright)^2=5

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

Solve for x

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

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

Steps by Finding Square Root

Take the square root of both sides of the equation.

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

Subtract 1 from both sides of the equation.

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

Subtracting 1 from itself leaves 0.

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

Subtract 1 from \sqrt{5}.

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

Subtract 1 from -\sqrt{5}.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide \sqrt{5}-1 by -1.

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

Divide -\sqrt{5}-1 by -1.

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

The equation is now solved.

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