Answer
$\{-1,15\}$
Work Step by Step
Taking the positive:
$$x-15=x^2-15x$$
$$0=x^2-16x+15$$
$$x^2-16x+15=0$$
$$(x-15)(x-1)=0$$
$$x-15=0$$
$$x=15$$
$$x-1=0$$
$$x=1$$
Checking:
For $x=15$:
$$|15-15|=(15)^2-15(15)$$
$$0=0~True$$
Thus, $x=15$ is a solution.
For $x=1$:
$$|1-15|=1^2-15(1)$$
$$14=-14~False$$
Thus, $x=1$ is not a solution.
Taking the negative:
$$x-15=-(x^2-15x)$$
$$x-15=-x^2+15x$$
$$x^2-14x-15=0$$
$$(x-15)(x+1)=0$$
$$x-15=0$$
$$x=15$$
$$x+1=0$$
$$x=-1$$
Checking for $x=-1$:
$$|-1-15|=(-1)^2-15(-1)$$
$$16=16~True$$
Thus, $x=-1$ is a solution.
Therefore, the solution set is:
$$\{-1,15\}$$
