Solve the quadratic equation. Write the smaller answer first. \( x^{2}-5 x=24 \) \( x=\square \) A \( x=\square \)

First, let's rearrange the equation \( x^{2}-5 x-24=0 \) to standard form. Now, we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} \), where \( a=1 \), \( b=-5 \), and \( c=-24 \). Plugging in the values, we find: 1. Calculate the discriminant: \( b^2 - 4ac = (-5)^2 - 4(1)(-24) = 25 + 96 = 121 \). 2. Now, the square root of the discriminant is \( \sqrt{121} = 11 \). 3. Plugging everything into the formula gives: \( x = \frac{5 \pm 11}{2} \). This leads to two solutions: - \( x = \frac{16}{2} = 8 \) - \( x = \frac{-6}{2} = -3 \) Thus, \( x=-3 \) A \( x=8 \).