c. \( -4 x^{2}-4 x=11 \)

To solve the quadratic equation \( -4x^{2} -4x = 11 \), start by rearranging it into standard form: \( -4x^{2} - 4x - 11 = 0 \). Now, you can factor or use the quadratic formula. Since factoring might not be straightforward, using the quadratic formula \( x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a} \) can be effective here. Plugging in \( a = -4 \), \( b = -4 \), and \( c = -11 \) will help you find those x-values, but watch out for negative signs! Once you have the solutions for \( x \), think about how those values fit into real-world contexts, like projectile motion or even analyzing profit margins in business. Quadratics pop up everywhere!