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

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

Solve for x

$$x = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Steps for Solving Linear Equation

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

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

Add 1 and 4 to get 5.

$$5-4x+x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$5-4x+x^{2}-x^{2}=0$$

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

$$5-4x=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-4x=-5$$

Divide both sides by -4.

$$x=\frac{-5}{-4}$$

Fraction \frac{-5}{-4} can be simplified to \frac{5}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{4}$$