Solve 15^2+x^2=(25-x)^2+10^2

$$15 ^ { 2 } + x ^ { 2 } = ( 25 - x ) ^ { 2 } + 10 ^ { 2 }$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Calculate 15 to the power of 2 and get 225.

$$225+x^{2}=\left(25-x\right)^{2}+10^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(25-x\right)^{2}.

$$225+x^{2}=625-50x+x^{2}+10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$225+x^{2}=625-50x+x^{2}+100$$

Add 625 and 100 to get 725.

$$225+x^{2}=725-50x+x^{2}$$

Add 50x to both sides.

$$225+x^{2}+50x=725+x^{2}$$

Subtract x^{2} from both sides.

$$225+x^{2}+50x-x^{2}=725$$

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

$$225+50x=725$$

Subtract 225 from both sides.

$$50x=725-225$$

Subtract 225 from 725 to get 500.

$$50x=500$$

Divide both sides by 50.

$$x=\frac{500}{50}$$

Divide 500 by 50 to get 10.

$$x=10$$