Use the quadratic formula to solve the equa \[ x^{2}+14 x=-49 \] \( x=\square \)

First, let's rewrite the equation in standard form by moving everything to one side: \[ x^2 + 14x + 49 = 0 \] Now, we can apply the quadratic formula, which is given by \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 1 \), \( b = 14 \), and \( c = 49 \). Plugging in these values: 1. Calculate the discriminant: \( b^2 - 4ac = 14^2 - 4(1)(49) = 196 - 196 = 0 \) 2. Since the discriminant is zero, there is exactly one solution: \( x = \frac{-14 \pm 0}{2(1)} = \frac{-14}{2} = -7 \) So, \( x = -7 \).