Solve the following equation. Enter your answers in numerical order. \( 8 r^{2}+96=-64 x \) \( x=\square \) and

To solve the equation \( 8r^{2} + 96 = -64x \), first, we can rearrange it to isolate \( x \): 1. Move \( 8r^{2} + 96 \) to the right side: \(-64x = - (8r^{2} + 96)\) \(-64x = -8r^{2} - 96\) 2. Divide both sides by -64 to solve for \( x \): \( x = \frac{8r^{2} + 96}{64} \) 3. Simplify the expression: \( x = \frac{8r^{2}}{64} + \frac{96}{64} = \frac{r^{2}}{8} + \frac{3}{2} \) So the solution for \( x \) is: \( x = \frac{r^{2}}{8} + \frac{3}{2} \) If you're looking for specific numerical examples, you could assign different values to \( r \) to get corresponding \( x \) values. For example: If \( r=0 \), then \( x = \frac{3}{2} \) If \( r=4 \), then \( x = \frac{4^2}{8} + \frac{3}{2} = \frac{16}{8} + \frac{3}{2} = 2 + \frac{3}{2} = 3.5 \) Thus, the answers are \( x = 1.5 \) and \( x = 3.5 \).