Solve 16-x^2=9-(5-x)^2

$$16 - x ^ { 2 } = 9 - ( 5 - x ) ^ { 2 }$$

Solve for x

$$x = \frac{16}{5} = 3\frac{1}{5} = 3.2$$

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}.

$$16-x^{2}=9-\left(25-10x+x^{2}\right)$$

To find the opposite of 25-10x+x^{2}, find the opposite of each term.

$$16-x^{2}=9-25+10x-x^{2}$$

Subtract 25 from 9 to get -16.

$$16-x^{2}=-16+10x-x^{2}$$

Subtract 10x from both sides.

$$16-x^{2}-10x=-16-x^{2}$$

Add x^{2} to both sides.

$$16-x^{2}-10x+x^{2}=-16$$

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

$$16-10x=-16$$

Subtract 16 from both sides.

$$-10x=-16-16$$

Subtract 16 from -16 to get -32.

$$-10x=-32$$

Divide both sides by -10.

$$x=\frac{-32}{-10}$$

Reduce the fraction \frac{-32}{-10} to lowest terms by extracting and canceling out -2.

$$x=\frac{16}{5}$$