n² + 5n + 4 = 0 Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. n =

To solve the quadratic equation ( n^2 + 5n + 4 = 0 ), we can factor the equation. We are looking for two numbers that multiply to ( 4 ) (the constant term) and add to ( 5 ) (the coefficient of ( n )). The numbers ( 1 ) and ( 4 ) meet these criteria.

So we can factor the equation as follows:

[

(n + 1)(n + 4) = 0

]

Now, set each factor equal to zero:

1. ( n + 1 = 0 ) → ( n = -1 )
2. ( n + 4 = 0 ) → ( n = -4 )

Thus, the solutions to the equation are:

[

n = -1, -4

]

These are the integer solutions of the equation. If you would like more help or in-depth assistance, feel free to check our extended services page!