SOLUTION: 5x(to the second power)+ 21x +4 =

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 5x(to the second power)+ 21x +4 =      Log On


   

Question 355685: 5x(to the second power)+ 21x +4 =
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you menat to include someting on the right side of the equality. I will further assume that was 0
5x%5E2+%2B+21x+%2B+4+=+0
%285x%2B1%29%28x%2B4%29+=+0
So either 5x%2B1=0 or x%2B4=0
Thus x = -1/5 or x = -4
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B21x%2B4+=+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=%2821%29%5E2-4%2A5%2A4=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-21%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2821%29%2Bsqrt%28+361+%29%29%2F2%5C5+=+-0.2
x%5B2%5D+=+%28-%2821%29-sqrt%28+361+%29%29%2F2%5C5+=+-4

Quadratic expression 5x%5E2%2B21x%2B4 can be factored:
5x%5E2%2B21x%2B4+=+5%28x--0.2%29%2A%28x--4%29
Again, the answer is: -0.2, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B21%2Ax%2B4+%29