Solve (x-5)^2-x^2=0

$$( x - 5 ) ^ { 2 } - x ^ { 2 } = 0$$

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-5\right)^{2}.

$$x^{2}-10x+25-x^{2}=0$$

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

$$-10x+25=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-10x=-25$$

Divide both sides by -10.

$$x=\frac{-25}{-10}$$

Reduce the fraction \frac{-25}{-10} to lowest terms by extracting and canceling out -5.

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