Final answer:
The quadratic equation 2u² + 3 = -7u can be solved by rearranging it to 2u² + 7u + 3 = 0 and applying the quadratic formula. Since there is an unknown squared, two solutions are expected, but it's crucial to verify their reasonableness within the problem's context.
Step-by-step explanation:
To solve the quadratic equation 2u² + 3 = -7u, we first need to rearrange the equation into standard form. We achieve this by adding 7u to both sides to get 2u² + 7u + 3 = 0. Next, we solve for 'u' either by factoring, using the quadratic formula, or completing the square.
The quadratic formula is √-b ± √(b² - 4ac) / 2a). In our equation, a = 2, b = 7, and c = 3. Substituting these values into the quadratic formula will yield the solutions for 'u'. Since it's a quadratic equation, there could be two solutions. It's important to check both solutions to ensure they are reasonable for the context of the problem.
Whenever an equation contains an unknown squared, we expect two solutions. However, both solutions may not always be valid in a physical context, as some solutions may not make sense when considering the constraints and implications of a real-world scenario.