Question

$z^{2}+10z - 24 = 0$
what is one of the solutions to the given equation?

Explanation:

Step1: Factor the quadratic equation

We find two numbers that multiply to $-24$ and add to $10$: $12$ and $-2$.
$z^2 + 10z - 24 = (z + 12)(z - 2) = 0$

Step2: Solve for $z$

Set each factor equal to 0:
$z + 12 = 0$ or $z - 2 = 0$

Step3: Calculate each solution

$z = -12$ or $z = 2$

Answer:

$z = 2$ (or $z = -12$ is also a valid solution)