Solve x^2+120^2=(5+x)^2

$$x ^ { 2 } + 120 ^ { 2 } = ( 5 + x ) ^ { 2 }$$

Solve for x

$$x = \frac{2875}{2} = 1437\frac{1}{2} = 1437.5$$

Steps for Solving Linear Equation

Calculate 120 to the power of 2 and get 14400.

$$x^{2}+14400=\left(5+x\right)^{2}$$

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

$$x^{2}+14400=25+10x+x^{2}$$

Subtract 10x from both sides.

$$x^{2}+14400-10x=25+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+14400-10x-x^{2}=25$$

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

$$14400-10x=25$$

Subtract 14400 from both sides.

$$-10x=25-14400$$

Subtract 14400 from 25 to get -14375.

$$-10x=-14375$$

Divide both sides by -10.

$$x=\frac{-14375}{-10}$$

Reduce the fraction \frac{-14375}{-10} to lowest terms by extracting and canceling out -5.

$$x=\frac{2875}{2}$$