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

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

Solve for x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps for Solving Linear Equation

Calculate 2 to the power of 2 and get 4.

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

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

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

Add 4 and 36 to get 40.

$$x^{2}=40-12x+x^{2}$$

Add 12x to both sides.

$$x^{2}+12x=40+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+12x-x^{2}=40$$

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

$$12x=40$$

Divide both sides by 12.

$$x=\frac{40}{12}$$

Reduce the fraction \frac{40}{12} to lowest terms by extracting and canceling out 4.

$$x=\frac{10}{3}$$