Question

use factoring to solve the quadratic equation. check by substitution or by using a graphing utility and identifying x-intercepts.
$x^2 - 5x - 14 = 0$
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 $-14$ and add to $-5$. These numbers are $-7$ and $2$.
$x^2 - 5x - 14 = (x - 7)(x + 2) = 0$

Step2: Apply zero product property

Set each factor equal to 0.
$x - 7 = 0$ or $x + 2 = 0$

Step3: Solve for x in each equation

For $x - 7 = 0$: $x = 7$
For $x + 2 = 0$: $x = -2$

Step4: Verify solutions (substitute back)

For $x=7$: $7^2 -5(7)-14=49-35-14=0$
For $x=-2$: $(-2)^2 -5(-2)-14=4+10-14=0$

Answer:

$\{-2, 7\}$