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.
- Calculate the discriminant (\(b^2 - 4ac\)):
\[ b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot (-8) = 9 + 32 = 41 \]
- 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:
- \( x_1 = \frac{-3 + \sqrt{41}}{2} \)
- \( x_2 = \frac{-3 - \sqrt{41}}{2} \)
You can enter \(x_1\) and \(x_2\) as your responses.