Question

use factoring to solve the quadratic equation. check by substitution or by using a graphing utility and identifying x-intercepts.
$x^2 - x - 72 = 0$
the solution set is
(type an integer or a simplified fraction. use a comma to separate answers as needed. type each solution only once.)

Explanation:

Step1: Factor the quadratic trinomial

We need two numbers that multiply to $-72$ and add to $-1$. These numbers are $-9$ and $8$, so:
$x^2 - x - 72 = (x - 9)(x + 8) = 0$

Step2: Apply zero product property

Set each factor equal to 0:
$x - 9 = 0$ or $x + 8 = 0$

Step3: Solve for x in each equation

For $x - 9 = 0$: $x = 9$
For $x + 8 = 0$: $x = -8$

Step4: Verify solutions (substitute back)

For $x=9$: $9^2 - 9 - 72 = 81 - 9 - 72 = 0$
For $x=-8$: $(-8)^2 - (-8) - 72 = 64 + 8 - 72 = 0$

Answer:

$\{-8, 9\}$