Question

Use the quadratic formula to solve 2x^2 + 5x + 3 = 0

Write your solutions as an integer and decimal rounded to the nearest hundredths if necessary.

X=
X=

Answer 1

To solve the quadratic equation \( 2x^2 + 5x + 3 = 0 \) using the quadratic formula, we start with the formula:

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

Here, the coefficients are:
- \( a = 2 \)
- \( b = 5 \)
- \( c = 3 \)

Now we can calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = 5^2 - 4 \cdot 2 \cdot 3 = 25 - 24 = 1
\]

Next, we substitute the values into the quadratic formula:

\[
x = \frac{-5 \pm \sqrt{1}}{2 \cdot 2}
\]

This simplifies to:

\[
x = \frac{-5 \pm 1}{4}
\]

Now we will calculate the two possible values for \( x \):

1. \( x = \frac{-5 + 1}{4} = \frac{-4}{4} = -1 \)
2. \( x = \frac{-5 - 1}{4} = \frac{-6}{4} = -\frac{3}{2} = -1.5 \)

Thus, the solutions to the equation \( 2x^2 + 5x + 3 = 0 \) are:

\[
x = -1 \text{ and } x = -1.5
\]

So we can summarize the solutions as follows:

\( X = -1 \) (integer)
\( X = -1.50 \) (decimal rounded to the nearest hundredths)