Question

20
Fill in the Blank 1 point
What are the solutions to the quadratic equation 3x2 + 15x - 18 = 0?
The solutions are choose your answer...

Answer 1

To find the solutions to the quadratic equation \(3x^2 + 15x - 18 = 0\), we can use the quadratic formula:

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

Where \(a = 3\), \(b = 15\), and \(c = -18\).

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

\[
b^2 - 4ac = 15^2 - 4 \cdot 3 \cdot (-18) = 225 + 216 = 441
\]

Now we can substitute the values into the quadratic formula:

\[
x = \frac{-15 \pm \sqrt{441}}{2 \cdot 3}
\]

\[
x = \frac{-15 \pm 21}{6}
\]

This gives us two potential solutions:

1.

\[
x = \frac{-15 + 21}{6} = \frac{6}{6} = 1
\]

2.

\[
x = \frac{-15 - 21}{6} = \frac{-36}{6} = -6
\]

Therefore, the solutions to the equation \(3x^2 + 15x - 18 = 0\) are:

**x = 1 and x = -6**.