Question

Using the quadratic formula, find the solution to 3x2+18x+24=0(1 point)Responsesx=−2, x=−4x=−2, x=−4x=4, x=2x=4, x=2x=−2x is equal to negative 2x=−4

Answer 1

To solve the quadratic equation \(3x^2 + 18x + 24 = 0\) using the quadratic formula, we start with the standard form of a quadratic equation:

\[
ax^2 + bx + c = 0
\]

Here, \(a = 3\), \(b = 18\), and \(c = 24\).

The quadratic formula is given by:

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

First, we need to calculate the discriminant \(b^2 - 4ac\):

\[
b^2 = 18^2 = 324
\]
\[
4ac = 4 \times 3 \times 24 = 288
\]
\[
b^2 - 4ac = 324 - 288 = 36
\]

Since the discriminant is positive, we will have two real solutions.

Now we can apply the quadratic formula:

\[
x = \frac{-18 \pm \sqrt{36}}{2 \times 3}
\]

Calculating the square root and the denominator:

\[
\sqrt{36} = 6
\]
\[
2a = 2 \times 3 = 6
\]

So, substituting back:

\[
x = \frac{-18 \pm 6}{6}
\]

Now we can find the two possible values for \(x\):

1. When using the positive sign:

\[
x = \frac{-18 + 6}{6} = \frac{-12}{6} = -2
\]

2. When using the negative sign:

\[
x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4
\]

Thus, the solutions are:

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

So the correct response is:

**x = -2, x = -4**