Solve 16-left(3-xright)^2=9-left(x+2right)^2

$$16- { \left(3-x \right) }^{ 2 } =9- { \left(x+2 \right) }^{ 2 }$$

Solve for x

$$x=-\frac{1}{5}=-0.2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3-x\right)^{2}.

$$16-\left(9-6x+x^{2}\right)=9-\left(x+2\right)^{2}$$

To find the opposite of 9-6x+x^{2}, find the opposite of each term.

$$16-9+6x-x^{2}=9-\left(x+2\right)^{2}$$

Subtract 9 from 16 to get 7.

$$7+6x-x^{2}=9-\left(x+2\right)^{2}$$

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

$$7+6x-x^{2}=9-\left(x^{2}+4x+4\right)$$

To find the opposite of x^{2}+4x+4, find the opposite of each term.

$$7+6x-x^{2}=9-x^{2}-4x-4$$

Subtract 4 from 9 to get 5.

$$7+6x-x^{2}=5-x^{2}-4x$$

Add x^{2} to both sides.

$$7+6x-x^{2}+x^{2}=5-4x$$

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

$$7+6x=5-4x$$

Add 4x to both sides.

$$7+6x+4x=5$$

Combine 6x and 4x to get 10x.

$$7+10x=5$$

Subtract 7 from both sides.

$$10x=5-7$$

Subtract 7 from 5 to get -2.

$$10x=-2$$

Divide both sides by 10.

$$x=\frac{-2}{10}$$

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

$$x=-\frac{1}{5}$$