Solve x^2=(5-x)^2+9

$$x ^ { 2 } = ( 5 - x ) ^ { 2 } + 9$$

Solve for x

$$x = \frac{17}{5} = 3\frac{2}{5} = 3.4$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-x\right)^{2}.

$$x^{2}=25-10x+x^{2}+9$$

Add 25 and 9 to get 34.

$$x^{2}=34-10x+x^{2}$$

Add 10x to both sides.

$$x^{2}+10x=34+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+10x-x^{2}=34$$

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

$$10x=34$$

Divide both sides by 10.

$$x=\frac{34}{10}$$

Reduce the fraction \frac{34}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{17}{5}$$