Solve (8+x)^2=12^2+x^2

$$( 8 + x ) ^ { 2 } = 12 ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8+x\right)^{2}.

$$64+16x+x^{2}=12^{2}+x^{2}$$

Calculate 12 to the power of 2 and get 144.

$$64+16x+x^{2}=144+x^{2}$$

Subtract x^{2} from both sides.

$$64+16x+x^{2}-x^{2}=144$$

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

$$64+16x=144$$

Subtract 64 from both sides.

$$16x=144-64$$

Subtract 64 from 144 to get 80.

$$16x=80$$

Divide both sides by 16.

$$x=\frac{80}{16}$$

Divide 80 by 16 to get 5.

$$x=5$$