d)

To solve the quadratic equation , we can use the quadratic formula . Here, , , and . Plugging these into the formula gives us . Therefore, the solutions are and .

Many mathematicians have found that the quadratic formula is not just useful for textbooks; it has real-world applications in fields like engineering and finance. For example, optimizing areas under curves and maximizing profit margins are scenarios where this formula comes in handy. It’s a key tool that helps professionals make informed decisions based on mathematical predictions!

However, when applying the quadratic formula, it’s easy to trip up by miscalculating the discriminant, . Double-check your arithmetic here! Another common mistake is forgetting to simplify square roots or fractions after substitution; doing so keeps your answers neat and easier to interpret. Always remember, clear fronts can lead to a clearer understanding!