Question

find the values of x that make the following equations equal to (x + 4)(x - 2)

x = -2 and x = 4

x = -2 and x = -4

x = 2 and x = 4

X = -4 and x = 2

Answer 1

To find the values of \(x\) that make the following equations equal to \((x + 4)(x - 2)\), we first need to expand the right side and set up an equation.

The expression \((x + 4)(x - 2)\) can be expanded as follows:

\[
(x + 4)(x - 2) = x^2 - 2x + 4x - 8 = x^2 + 2x - 8
\]

Next, we will set this equal to zero:

\[
x^2 + 2x - 8 = 0
\]

Now, we solve this quadratic equation using the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \(a = 1\), \(b = 2\), and \(c = -8\).

First, we calculate the discriminant:

\[
b^2 - 4ac = 2^2 - 4(1)(-8) = 4 + 32 = 36
\]

Now we can find the roots:

\[
x = \frac{-2 \pm \sqrt{36}}{2 \cdot 1} = \frac{-2 \pm 6}{2}
\]

Calculating the two possible values for \(x\):

1. \(x = \frac{-2 + 6}{2} = \frac{4}{2} = 2\)

2. \(x = \frac{-2 - 6}{2} = \frac{-8}{2} = -4\)

Thus, the solutions are:

\[
x = 2 \quad \text{and} \quad x = -4
\]

Looking at the options provided:

- **x = -2 and x = 4**
- **x = -2 and x = -4**
- **x = 2 and x = 4**
- **x = -4 and x = 2**

The correct values are:

\[
\boxed{-4 \text{ and } 2}
\]