Use the quadratic formula to solve the \[ x^{2}+10 x+9=0 \] \( x= \)

To solve the quadratic equation \( x^{2}+10x+9=0 \) using the quadratic formula, which is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), let's first identify the coefficients: \( a = 1 \), \( b = 10 \), and \( c = 9 \). Now, plug these values into the formula. Begin with calculating the discriminant: 1. Calculate \( b^2 - 4ac \): \( 10^2 - 4(1)(9) = 100 - 36 = 64 \) 2. Now apply the quadratic formula: \( x = \frac{-10 \pm \sqrt{64}}{2(1)} = \frac{-10 \pm 8}{2} \) This gives us two possible solutions: - \( x = \frac{-10 + 8}{2} = \frac{-2}{2} = -1 \) - \( x = \frac{-10 - 8}{2} = \frac{-18}{2} = -9 \) Thus, the solutions are: \( x = -1 \) or \( x = -9 \).