There is no two numbers that can add to 10 and multiply to 28, the highest number you can get by multiplying numbers that add to equal 10 are 5 and 5, and that only reaches 25. I'm sorry
First lets distribute the 5x
5x^2 + 30x = -50
Lets divide every term by 5
x^2 + 6x = -10
To complete the square we have to half the b value, which in this case is 6. Then square it.
Half of 6 is 3, 3 squared is 9
Add that to both sides of the equation
x^2 + 6x + 9 = -1
Find the binomial squared
(x+3)^2 (If you're wondering how i got that please comment)
(x+3)^2 = -1
Take the square root of the equation of both sides
(x+3) = +/- i
x = -3 +/- i
x = -3 - i
and
x = -3 + i
This DE has characteristic equation
with a repeated root at r = 3/2. Then the characteristic solution is
which has derivative
Use the given initial conditions to solve for the constants:
and so the particular solution to the IVP is
If you mean that you want to solve the equation for v, then all you need to do is to multiply both sides by 3:
The answer to you question is B
