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Use the quadratic formula to answer the questions below.

Quadratic Formula is x=−b ± b2−4ac√2a


The equation is 3x2+18x+24=0


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Answer 1

To solve the quadratic equation \(3x^2 + 18x + 24 = 0\) using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), we first need to identify the values of \(a\), \(b\), and \(c\):

- \(a = 3\)
- \(b = 18\)
- \(c = 24\)

Next, we will calculate the discriminant (\(b^2 - 4ac\)):

1. Calculate \(b^2\):
\[
b^2 = 18^2 = 324
\]

2. Calculate \(4ac\):
\[
4ac = 4 \cdot 3 \cdot 24 = 288
\]

3. Calculate \(b^2 - 4ac\):
\[
b^2 - 4ac = 324 - 288 = 36
\]

Now we substitute \(a\), \(b\), and the discriminant into the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-18 \pm \sqrt{36}}{2 \cdot 3}
\]

4. Calculate \(\sqrt{36}\):
\[
\sqrt{36} = 6
\]

Now substitute this back into the formula:

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

5. This gives us two possible solutions for \(x\):

- When using the plus sign:
\[
x = \frac{-18 + 6}{6} = \frac{-12}{6} = -2
\]

- When using the minus sign:
\[
x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4
\]

So, the solutions to the equation \(3x^2 + 18x + 24 = 0\) are:

**Answers:**
- \(x_1 = -2\)
- \(x_2 = -4\)

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