For what values of x is x² + 2x = 24 true?
-6 and -4, -4 and 6, 4 and -6, 6 and 4

Solution:

The quadratic equation x² + 2x = 24 can be written in the standard form x² + 2x - 24 = 0.

Let us factorize the equation to find the value of x by splitting the middle term.

Step 1: Identify the values of a, b and c.

In the above equation, a is coefficient of x² = 1, b is the coefficient of x = 2 and c is the constant term = -24.

Step 2: Multiply a and c and find the factors that add up to b.

1 × (-24) = -24

⇒ 6 and -4 are the factors that add up to b.

Step 3: Split bx into two terms.

x² + 6x - 4x - 24 = 0

Step 4: Take out the common factors by grouping.

x(x + 6) - 4(x + 6) = 0

(x - 4)(x + 6) = 0

By putting the factors equal to zero we get two values of x

x - 4 = 0 and x + 6 = 0

x = 4 and x = -6

Thus, the two values that satisfy the equation are 4 and -6.

---

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

Summary:

For the value of x = 4 and -6, the equation x² + 2x = 24 is true.