Solve x^2+36=left(9-xright)^2

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

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(9-x\right)^{2}.

$$x^{2}+36=81-18x+x^{2}$$

Add 18x to both sides.

$$x^{2}+36+18x=81+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+36+18x-x^{2}=81$$

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

$$36+18x=81$$

Subtract 36 from both sides.

$$18x=81-36$$

Subtract 36 from 81 to get 45.

$$18x=45$$

Divide both sides by 18.

$$x=\frac{45}{18}$$

Reduce the fraction \frac{45}{18} to lowest terms by extracting and canceling out 9.

$$x=\frac{5}{2}$$