Question

Use the quadratic formula to solve the equation.
x squared plus 3 x minus 8 equals 0x2+3x−8=0
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Question content area right
Part 1
xequals=enter your response here
​(Simplify your answer. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.)

Answer 1

To solve the quadratic equation \( x^2 + 3x - 8 = 0 \) using the quadratic formula, we use the formula:

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

Here, the coefficients are:
- \( a = 1 \)
- \( b = 3 \)
- \( c = -8 \)

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

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

Now, substitute \( a \), \( b \), and the discriminant back into the formula:

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

This simplifies to:

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

Thus, the two solutions are:

\[
x = \frac{-3 + \sqrt{41}}{2}, \quad x = \frac{-3 - \sqrt{41}}{2}
\]

In conclusion, your answer is:

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

You can enter this as:

\((-3 + \sqrt{41})/2, (-3 - \sqrt{41})/2\)