Solve left(x-1right)^2=7-2x

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

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$x^{2}-2x+1=7-2x$$

Add 2x to both sides.

$$x^{2}-2x+1+2x=7$$

Combine -2x and 2x to get 0.

$$x^{2}+1=7$$

Subtract 1 from both sides.

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

Subtract 1 from 7 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$x^{2}-2x+1=7-2x$$

Subtract 7 from both sides.

$$x^{2}-2x+1-7=-2x$$

Subtract 7 from 1 to get -6.

$$x^{2}-2x-6=-2x$$

Add 2x to both sides.

$$x^{2}-2x-6+2x=0$$

Combine -2x and 2x to get 0.

$$x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)}}{2}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24}}{2}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{2} when ± is plus.

$$x=\sqrt{6}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{2} when ± is minus.

$$x=-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6} x=-\sqrt{6}$$