Solve (6-x)^2+3^2=(3+x)^2

$$( 6 - x ) ^ { 2 } + 3 ^ { 2 } = ( 3 + x ) ^ { 2 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-x\right)^{2}.

$$36-12x+x^{2}+3^{2}=\left(3+x\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$36-12x+x^{2}+9=\left(3+x\right)^{2}$$

Add 36 and 9 to get 45.

$$45-12x+x^{2}=\left(3+x\right)^{2}$$

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

$$45-12x+x^{2}=9+6x+x^{2}$$

Subtract 6x from both sides.

$$45-12x+x^{2}-6x=9+x^{2}$$

Combine -12x and -6x to get -18x.

$$45-18x+x^{2}=9+x^{2}$$

Subtract x^{2} from both sides.

$$45-18x+x^{2}-x^{2}=9$$

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

$$45-18x=9$$

Subtract 45 from both sides.

$$-18x=9-45$$

Subtract 45 from 9 to get -36.

$$-18x=-36$$

Divide both sides by -18.

$$x=\frac{-36}{-18}$$

Divide -36 by -18 to get 2.

$$x=2$$