Solve (5+x)^2=(8)^2+(3+x)^2

$$( 5 + x ) ^ { 2 } = ( 8 ) ^ { 2 } + ( 3 + x ) ^ { 2 }$$

Solve for x

$$x=12$$

Steps for Solving Linear Equation

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

$$25+10x+x^{2}=8^{2}+\left(3+x\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$25+10x+x^{2}=64+\left(3+x\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+x\right)^{2}.

$$25+10x+x^{2}=64+9+6x+x^{2}$$

Add 64 and 9 to get 73.

$$25+10x+x^{2}=73+6x+x^{2}$$

Subtract 6x from both sides.

$$25+10x+x^{2}-6x=73+x^{2}$$

Combine 10x and -6x to get 4x.

$$25+4x+x^{2}=73+x^{2}$$

Subtract x^{2} from both sides.

$$25+4x+x^{2}-x^{2}=73$$

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

$$25+4x=73$$

Subtract 25 from both sides.

$$4x=73-25$$

Subtract 25 from 73 to get 48.

$$4x=48$$

Divide both sides by 4.

$$x=\frac{48}{4}$$

Divide 48 by 4 to get 12.

$$x=12$$