Solve x^2+3^2=left(5-xright)^2

$${ x }^{ 2 } + { 3 }^{ 2 } = { \left(5-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{8}{5} = 1\frac{3}{5} = 1.6$$

Steps for Solving Linear Equation

Calculate 3 to the power of 2 and get 9.

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

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

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

Add 10x to both sides.

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

Subtract x^{2} from both sides.

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

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

$$9+10x=25$$

Subtract 9 from both sides.

$$10x=25-9$$

Subtract 9 from 25 to get 16.

$$10x=16$$

Divide both sides by 10.

$$x=\frac{16}{10}$$

Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{8}{5}$$