Question

Use the quadratic formula to solve 2x2+5x+3=0 . Round your answer to the tenths, if necessary. Reference Sheet - Quadratic Formula (2 points) x= x=

Answer 1

To solve the quadratic equation \(2x^2 + 5x + 3 = 0\) using the quadratic formula, we first identify the coefficients \(a\), \(b\), and \(c\):

- \(a = 2\)
- \(b = 5\)
- \(c = 3\)

The quadratic formula is given by:

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

Now let's calculate the discriminant \(b^2 - 4ac\):

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

Now we can substitute \(b\) and the calculated discriminant back into the quadratic formula:

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

Since \(\sqrt{1} = 1\), we have:

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

This gives us two potential solutions 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 rounded to the tenths are:

\[
x = -1.0 \quad \text{and} \quad x = -1.5
\]

So the final answers are:

\[
x = -1.0 \quad \text{and} \quad x = -1.5
\]