Solve 4+(x-1)^2=x^2

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

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

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}.

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

Add 4 and 1 to get 5.

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

Subtract x^{2} from both sides.

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

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

$$5-2x=0$$

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

$$-2x=-5$$

Divide both sides by -2.

$$x=\frac{-5}{-2}$$

Fraction \frac{-5}{-2} can be simplified to \frac{5}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{2}$$