Solve (x)^2+(10)^2=(x+5)^2

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

Solve for x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps for Solving Linear Equation

Calculate 10 to the power of 2 and get 100.

$$x^{2}+100=\left(x+5\right)^{2}$$

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

$$x^{2}+100=x^{2}+10x+25$$

Subtract x^{2} from both sides.

$$x^{2}+100-x^{2}=10x+25$$

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

$$100=10x+25$$

Swap sides so that all variable terms are on the left hand side.

$$10x+25=100$$

Subtract 25 from both sides.

$$10x=100-25$$

Subtract 25 from 100 to get 75.

$$10x=75$$

Divide both sides by 10.

$$x=\frac{75}{10}$$

Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$x=\frac{15}{2}$$