Using the quadratic formula, find the solution to 3x^2+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 will first identify the coefficients:

• $a=3$
• $b=18$
• $c=24$

The quadratic formula is given by:

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

Now, let's calculate the discriminant:

$$b^2-4ac={18}^2-4\cdot 3\cdot 24=324-288=36$$

Now that we have the discriminant, we can plug it into the formula:

$$x=\frac{-18\pm \sqrt{36}}{2\cdot 3}$$

Calculating the square root of 36:

$$\sqrt{36}=6$$

Now substituting that back into the equation:

$$x=\frac{-18\pm 6}{6}$$

Now, we will calculate the two possible values for $x$:

1. Using the plus sign:

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

2. Using the minus sign:

$$x=\frac{-18-6}{6}=\frac{-24}{6}=-4$$

Thus, the solutions to the equation $3x^2+18x+24=0$ are:

$$x=-2\text{and}x=-4$$

So the correct response is:

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