Use the quadratic formula to solve the equation.

Question

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.