Solve the quadratic equation. x ^ 2 + 9x - 15 = 0 (1 point) O x = (9 plus/minus sqrt(21))/2 O x = (9 plus/minus sqrt(141))/2; x = (- 9 plus/minus sqrt(141))/2; x = (- 9 plus/minus sqrt(21))/2

Answer 1

To solve the quadratic equation \( x^2 + 9x - 15 = 0 \), we can use the quadratic formula:

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

Here, \( a = 1 \), \( b = 9 \), and \( c = -15 \).

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

\[ b^2 = 9^2 = 81 \] \[ 4ac = 4 \cdot 1 \cdot (-15) = -60 \] \[ b^2 - 4ac = 81 - (-60) = 81 + 60 = 141 \]

2. Now, substitute \( a \), \( b \), and the discriminant into the quadratic formula:

\[ x = \frac{-9 \pm \sqrt{141}}{2 \cdot 1} = \frac{-9 \pm \sqrt{141}}{2} \]

Thus, the solutions to the quadratic equation are:

\[ x = \frac{-9 + \sqrt{141}}{2}, \quad x = \frac{-9 - \sqrt{141}}{2} \]

The correct option in your provided choices corresponds to:

\( x = \frac{-9 \pm \sqrt{141}}{2} \).