Question

solve for x. $x^2 + 2x - 48 = 0$ $x = 0$ $x = 6$ $x = 6$ or $x = -8$ $x = -6$ or $x = 8$

Explanation:

Step1: Factor the quadratic equation

We need two numbers that multiply to $-48$ and add to $2$. These numbers are $8$ and $-6$.
$x^2 + 2x - 48 = (x + 8)(x - 6) = 0$

Step2: Set each factor equal to 0

For a product of factors to be 0, at least one factor must be 0.
$x + 8 = 0$ or $x - 6 = 0$

Step3: Solve for x in each equation

Solve $x + 8 = 0$: $x = -8$
Solve $x - 6 = 0$: $x = 6$

Answer:

$x = 6$ or $x = -8$