Solve 81+x^2=left(27-xright)^2

$$81+ { x }^{ 2 } = { \left(27-x \right) }^{ 2 }$$

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(27-x\right)^{2}.

$$81+x^{2}=729-54x+x^{2}$$

Add 54x to both sides.

$$81+x^{2}+54x=729+x^{2}$$

Subtract x^{2} from both sides.

$$81+x^{2}+54x-x^{2}=729$$

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

$$81+54x=729$$

Subtract 81 from both sides.

$$54x=729-81$$

Subtract 81 from 729 to get 648.

$$54x=648$$

Divide both sides by 54.

$$x=\frac{648}{54}$$

Divide 648 by 54 to get 12.

$$x=12$$