Using the quadratic formula, find the solution to 3x2+18x+24=0

Question

.(1 point)
Responses

x=−2
x equals negative 2

x=−2
, x=−4
x equals negative 2 , x equals negative 4

x=4
, x=2
x equals 4 , x equals 2

x=−4

Answer 1

To solve the quadratic equation \(3x^2 + 18x + 24 = 0\) using the quadratic formula, we start by identifying the coefficients:

• \(a = 3\)
• \(b = 18\)
• \(c = 24\)

The quadratic formula is given by:

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

Now we substitute the values of \(a\), \(b\), and \(c\) into the formula.

1. Calculate the discriminant (\(b^2 - 4ac\)):

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

2. Now substitute \(b\) and the discriminant into the quadratic formula:

\[ x = \frac{{-18 \pm \sqrt{36}}}{2 \cdot 3} \] \[ x = \frac{{-18 \pm 6}}{6} \]

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

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

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

Thus, the solutions are:

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

Therefore, the correct response is:

x = -2, x = -4