Ashlee Lange Solve for \( s \). Separate multiple answers with a comma. \[ 896 s^{2}=-512 s^{3}-392 s \]

First, let's rearrange the equation to bring all terms to one side: \[ 896 s^2 + 512 s^3 + 392 s = 0. \] Now, we can factor out the common term, which is \( s \): \[ s (512 s^2 + 896 s + 392) = 0. \] So, one solution is \( s = 0 \). Now we need to solve the quadratic equation \( 512 s^2 + 896 s + 392 = 0 \). We can use the quadratic formula \( s = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 512 \), \( b = 896 \), and \( c = 392 \). Calculating the discriminant: \[ b^2 - 4ac = 896^2 - 4(512)(392). \] Calculating the individual components: - \( 896^2 = 802816 \) - \( 4(512)(392) = 802816 \) So the discriminant is: \[ 802816 - 802816 = 0. \] Since the discriminant is zero, there is one real double root: \[ s = \frac{-896}{2 \cdot 512} = \frac{-896}{1024} = -\frac{7}{8}. \] Thus, the solutions for \( s \) are: \[ s = 0, -\frac{7}{8}. \]