Solve the equation. (Enter your answers as a comma-separated list.) \[ x^{2}+4 x-21=0 \] SUBMIT ANSWER

To solve the equation \( x^2 + 4x - 21 = 0 \), we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 4 \), and \( c = -21 \). First, we calculate the discriminant: \[ b^2 - 4ac = 4^2 - 4 \cdot 1 \cdot (-21) = 16 + 84 = 100 \] Now, substituting into the quadratic formula: \[ x = \frac{-4 \pm \sqrt{100}}{2 \cdot 1} = \frac{-4 \pm 10}{2} \] Calculating the two possible values for \( x \): 1. \( x = \frac{-4 + 10}{2} = \frac{6}{2} = 3 \) 2. \( x = \frac{-4 - 10}{2} = \frac{-14}{2} = -7 \) So, the solutions to the equation are \( 3, -7 \).