Question

Use the quadratic formula to solve the equation.
x squared plus 3 x minus 8 equals 0
.
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Part 1
xequals
  
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Answer 1

To solve the quadratic equation \( x^2 + 3x - 8 = 0 \) using the quadratic formula, we first identify the coefficients \(a\), \(b\), and \(c\):

- \(a = 1\)
- \(b = 3\)
- \(c = -8\)

The quadratic formula is given by:

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

Now, we can substitute the values of \(a\), \(b\), and \(c\) into the formula.

1. Calculate the discriminant (\(b^2 - 4ac\)):

\[
b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot (-8) = 9 + 32 = 41
\]

2. Substitute \(b\), the square root of the discriminant, and \(a\) into the quadratic formula:

\[
x = \frac{-3 \pm \sqrt{41}}{2 \cdot 1} = \frac{-3 \pm \sqrt{41}}{2}
\]

Now, we have two possible solutions for \(x\):

\[
x_1 = \frac{-3 + \sqrt{41}}{2}
\]

\[
x_2 = \frac{-3 - \sqrt{41}}{2}
\]

Thus, the solutions to the equation \( x^2 + 3x - 8 = 0 \) are:

1. \( x_1 = \frac{-3 + \sqrt{41}}{2} \)
2. \( x_2 = \frac{-3 - \sqrt{41}}{2} \)

You can enter \(x_1\) and \(x_2\) as your responses.