Solve (x-1)^2=7

$$( x - 1 ) ^ { 2 } = 7$$

Solve for x

$$x=\sqrt{7}+1\approx 3.645751311$$

$$x=1-\sqrt{7}\approx -1.645751311$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-1=\sqrt{7} x-1=-\sqrt{7}$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=\sqrt{7}-\left(-1\right) x-1-\left(-1\right)=-\sqrt{7}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=\sqrt{7}-\left(-1\right) x=-\sqrt{7}-\left(-1\right)$$

Subtract -1 from \sqrt{7}.

$$x=\sqrt{7}+1$$

Subtract -1 from -\sqrt{7}.

$$x=1-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7}+1 x=1-\sqrt{7}$$