Solve 4+x^2=left(6-xright)^2

$$4+ { x }^{ 2 } = { \left(6-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

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}.

$$4+x^{2}=36-12x+x^{2}$$

Add 12x to both sides.

$$4+x^{2}+12x=36+x^{2}$$

Subtract x^{2} from both sides.

$$4+x^{2}+12x-x^{2}=36$$

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

$$4+12x=36$$

Subtract 4 from both sides.

$$12x=36-4$$

Subtract 4 from 36 to get 32.

$$12x=32$$

Divide both sides by 12.

$$x=\frac{32}{12}$$

Reduce the fraction \frac{32}{12} to lowest terms by extracting and canceling out 4.

$$x=\frac{8}{3}$$