Solve x^2=left(6-xright)^2+9

$${ x }^{ 2 } = { \left(6-x \right) }^{ 2 } +9$$

Solve for x

$$x = \frac{15}{4} = 3\frac{3}{4} = 3.75$$

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}.

$$x^{2}=36-12x+x^{2}+9$$

Add 36 and 9 to get 45.

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

Add 12x to both sides.

$$x^{2}+12x=45+x^{2}$$

Subtract x^{2} from both sides.

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

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

$$12x=45$$

Divide both sides by 12.

$$x=\frac{45}{12}$$

Reduce the fraction \frac{45}{12} to lowest terms by extracting and canceling out 3.

$$x=\frac{15}{4}$$