Solve 75+(10-x)^2=(5+x)^2-25

$$75 + ( 10 - x ) ^ { 2 } = ( 5 + x ) ^ { 2 } - 25$$

Solve for x

$$x = \frac{35}{6} = 5\frac{5}{6} \approx 5.833333333$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10-x\right)^{2}.

$$75+100-20x+x^{2}=\left(5+x\right)^{2}-25$$

Add 75 and 100 to get 175.

$$175-20x+x^{2}=\left(5+x\right)^{2}-25$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5+x\right)^{2}.

$$175-20x+x^{2}=25+10x+x^{2}-25$$

Subtract 25 from 25 to get 0.

$$175-20x+x^{2}=10x+x^{2}$$

Subtract 10x from both sides.

$$175-20x+x^{2}-10x=x^{2}$$

Combine -20x and -10x to get -30x.

$$175-30x+x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$175-30x+x^{2}-x^{2}=0$$

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

$$175-30x=0$$

Subtract 175 from both sides. Anything subtracted from zero gives its negation.

$$-30x=-175$$

Divide both sides by -30.

$$x=\frac{-175}{-30}$$

Reduce the fraction \frac{-175}{-30} to lowest terms by extracting and canceling out -5.

$$x=\frac{35}{6}$$