Solve 5^2+left(10+xright)^2=left(15-xright)^2

$${ 5 }^{ 2 } + { \left(10+x \right) }^{ 2 } = { \left(15-x \right) }^{ 2 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Calculate 5 to the power of 2 and get 25.

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

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

$$25+100+20x+x^{2}=\left(15-x\right)^{2}$$

Add 25 and 100 to get 125.

$$125+20x+x^{2}=\left(15-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(15-x\right)^{2}.

$$125+20x+x^{2}=225-30x+x^{2}$$

Add 30x to both sides.

$$125+20x+x^{2}+30x=225+x^{2}$$

Combine 20x and 30x to get 50x.

$$125+50x+x^{2}=225+x^{2}$$

Subtract x^{2} from both sides.

$$125+50x+x^{2}-x^{2}=225$$

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

$$125+50x=225$$

Subtract 125 from both sides.

$$50x=225-125$$

Subtract 125 from 225 to get 100.

$$50x=100$$

Divide both sides by 50.

$$x=\frac{100}{50}$$

Divide 100 by 50 to get 2.

$$x=2$$