What is an equation that has solutions m = 5 and m = 9?

To find an equation that has specific solutions, such as m = 5 and m = 9, we can use the concept of factored forms in algebra. The general approach is to create a polynomial equation where the specific solutions are the roots.

In this case, we can create the equation by finding the factors corresponding to the roots. If m = 5 and m = 9 are the roots, we can express this as:

(m - 5)(m - 9) = 0

Next, we can expand this equation:

m^2 - 9m - 5m + 45 = 0

Combining like terms gives us:

m^2 - 14m + 45 = 0

Thus, an equation that has solutions of m = 5 and m = 9 is:

m^2 - 14m + 45 = 0

This quadratic equation can be verified by plugging the values of m back into the equation to ensure both solutions satisfy it. If you substitute m = 5 or m = 9, the left-hand side will equal zero, confirming that these are indeed the correct roots.