Question

use factoring to solve the quadratic equation. check by substitution or by using a graphing utility and identifying x-intercepts.
$x^2 - 2x - 48 = 0$
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 $-48$ and add to $-2$. These numbers are $-8$ and $6$. So:
$x^2 - 2x - 48 = (x - 8)(x + 6) = 0$

Step2: Apply zero product property

Set each factor equal to 0:
$x - 8 = 0$ or $x + 6 = 0$

Step3: Solve for $x$

For $x - 8 = 0$, we get $x = 8$. For $x + 6 = 0$, we get $x = -6$.

Step4: Verify solutions (substitute back)

Substitute $x=8$: $8^2 - 2(8) - 48 = 64 - 16 - 48 = 0$. Substitute $x=-6$: $(-6)^2 - 2(-6) - 48 = 36 + 12 - 48 = 0$. Both satisfy the equation.

Answer:

$\{-6, 8\}$