For what values of x is x² – 2x – 24 = 0 true?

To find the values of x for the equation x² – 2x – 24 = 0, we need to factor or use the quadratic formula.

First, let’s try to factor the quadratic. We are looking for two numbers that multiply to -24 (the constant term) and add up to -2 (the coefficient of x). The numbers -6 and +4 fit this requirement because:

• -6 * 4 = -24
• -6 + 4 = -2

We can write the equation as:

(x – 6)(x + 4) = 0

Setting each factor to zero gives us the possible solutions:

1. x – 6 = 0 → x = 6
2. x + 4 = 0 → x = -4

Thus, the values of x that satisfy the equation x² – 2x – 24 = 0 are:

x = 6 and x = -4.