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

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

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

Calculate 2 to the power of 2 and get 4.

$$x^{2}-2x+1+4=x^{2}+1$$

Add 1 and 4 to get 5.

$$x^{2}-2x+5=x^{2}+1$$

Subtract x^{2} from both sides.

$$x^{2}-2x+5-x^{2}=1$$

Combine x^{2} and -x^{2} to get 0.

$$-2x+5=1$$

Subtract 5 from both sides.

$$-2x=1-5$$

Subtract 5 from 1 to get -4.

$$-2x=-4$$

Divide both sides by -2.

$$x=\frac{-4}{-2}$$

Divide -4 by -2 to get 2.

$$x=2$$