Question

Use the quadratic formula to solve the equation.
x squared plus 3 x minus 6 equals 0
.
.
.
Question content area right
Part 1
xequals
  
enter your response here

Answer 1

To solve the quadratic equation \( x^2 + 3x - 6 = 0 \) using the quadratic formula, we will use the formula:

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

In this equation \( a = 1 \), \( b = 3 \), and \( c = -6 \).

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

\[
b^2 = 3^2 = 9
\]
\[
4ac = 4 \cdot 1 \cdot (-6) = -24
\]
\[
b^2 - 4ac = 9 - (-24) = 9 + 24 = 33
\]

Now, we substitute the values into the quadratic formula:

\[
x = \frac{-3 \pm \sqrt{33}}{2 \cdot 1}
\]
\[
x = \frac{-3 \pm \sqrt{33}}{2}
\]

This gives us the two solutions:

\[
x = \frac{-3 + \sqrt{33}}{2} \quad \text{and} \quad x = \frac{-3 - \sqrt{33}}{2}
\]

So the solutions to the equation \( x^2 + 3x - 6 = 0 \) are:

\[
x = \frac{-3 + \sqrt{33}}{2} \quad \text{or} \quad x = \frac{-3 - \sqrt{33}}{2}
\]

If you want numerical approximations:

\[
x \approx 0.372 \quad \text{and} \quad x \approx -6.372
\]