Solve 5^2+(4+x)^2=(5+x)^2

$$5 ^ { 2 } + ( 4 + x ) ^ { 2 } = ( 5 + x ) ^ { 2 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Calculate 5 to the power of 2 and get 25.

$$25+\left(4+x\right)^{2}=\left(5+x\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4+x\right)^{2}.

$$25+16+8x+x^{2}=\left(5+x\right)^{2}$$

Add 25 and 16 to get 41.

$$41+8x+x^{2}=\left(5+x\right)^{2}$$

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

$$41+8x+x^{2}=25+10x+x^{2}$$

Subtract 10x from both sides.

$$41+8x+x^{2}-10x=25+x^{2}$$

Combine 8x and -10x to get -2x.

$$41-2x+x^{2}=25+x^{2}$$

Subtract x^{2} from both sides.

$$41-2x+x^{2}-x^{2}=25$$

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

$$41-2x=25$$

Subtract 41 from both sides.

$$-2x=25-41$$

Subtract 41 from 25 to get -16.

$$-2x=-16$$

Divide both sides by -2.

$$x=\frac{-16}{-2}$$

Divide -16 by -2 to get 8.

$$x=8$$