Solve (x+10)^2=x^2+(50)^2

$$( x + 10 ) ^ { 2 } = x ^ { 2 } + ( 50 ) ^ { 2 }$$

Solve for x

$$x=120$$

Steps for Solving Linear Equation

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

$$x^{2}+20x+100=x^{2}+50^{2}$$

Calculate 50 to the power of 2 and get 2500.

$$x^{2}+20x+100=x^{2}+2500$$

Subtract x^{2} from both sides.

$$x^{2}+20x+100-x^{2}=2500$$

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

$$20x+100=2500$$

Subtract 100 from both sides.

$$20x=2500-100$$

Subtract 100 from 2500 to get 2400.

$$20x=2400$$

Divide both sides by 20.

$$x=\frac{2400}{20}$$

Divide 2400 by 20 to get 120.

$$x=120$$