Final Answer:
The solutions (u = 0) and (u = -41) are obtained by factoring the quadratic equation (u ² + 41u = 0 into u(u + 41) = 0. Setting each factor to zero gives the solutions, confirming that (u = 0) and (u = -41) satisfy the equation.
Step-by-step explanation:
To find the solutions for u we can factor the equation(u² + 41u = 0\) as (u(u + 41) = 0). This implies that either u = 0) or (u + 41 = 0).
Setting the first factor to zero gives u = 0. For the second factor, solving u + 41 = 0 results in u = -41. Therefore, the solutions to the quadratic equation are u = 0) and u = -41.
This means that when u = 0, the equation is satisfied, and when \(u = -41\), the equation is also satisfied. These are the values for u that make the equation (u² + 41u = 0) true.
In summary, the solutions to the quadratic equation (u² + 41u = 0 aru = 0 and (u = -41, and these values satisfy the equation when substituted back into it.