SOLUTION: What two number mulitply to -64 and add to be -5

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: What two number mulitply to -64 and add to be -5      Log On


   

Question 803802: What two number mulitply to -64 and add to be -5
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What two number mulitply to -64 and add to be -5
-----------
x*y = -64
x + y = -5 --> y = -5-x
x*(-5-x) = -64
x*(x+5) = 64
x%5E2+%2B+5x+-+64+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-64+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A1%2A-64=281.

Discriminant d=281 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+281+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+281+%29%29%2F2%5C1+=+5.88152730712011
x%5B2%5D+=+%28-%285%29-sqrt%28+281+%29%29%2F2%5C1+=+-10.8815273071201

Quadratic expression 1x%5E2%2B5x%2B-64 can be factored:
1x%5E2%2B5x%2B-64+=+%28x-5.88152730712011%29%2A%28x--10.8815273071201%29
Again, the answer is: 5.88152730712011, -10.8815273071201. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-64+%29

=================
x = one of the solutions above, y = the other one.