Question

solve the following equation.
$v^2 + 3v - 40 = 0$
select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
a. the solution(s) is/are $v = $ (simplify your answer. type an integer or a fraction. use a comma to separate answers as needed)
b. there are no real solutions.

Explanation:

Step1: Factor the quadratic equation

We need two numbers that multiply to $-40$ and add to $3$. These numbers are $8$ and $-5$.
$v^2 + 3v - 40 = (v + 8)(v - 5) = 0$

Step2: Solve for $v$

Set each factor equal to 0 and solve.
For $v + 8 = 0$: $v = -8$
For $v - 5 = 0$: $v = 5$

Answer:

A. The solution(s) is/are $v = -8, 5$