SOLUTION: Hello. I am having a problem factoring this equation and I am asking for your help. The equation is: 4x^2-8x-21 I tried multiplying -21x4 which = -84 , but I can't seem to find t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello. I am having a problem factoring this equation and I am asking for your help. The equation is: 4x^2-8x-21 I tried multiplying -21x4 which = -84 , but I can't seem to find t      Log On


   

Question 989512: Hello. I am having a problem factoring this equation and I am asking for your help. The equation is:
4x^2-8x-21
I tried multiplying -21x4 which = -84 , but I can't seem to find the 2 terms that make -8. Am I just confusing myself or is it staring me in the face? Please help me.
Found 4 solutions by macston, solver91311, MathTherapy, Alan3354:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
4x%5E2-8x-21=%284x%2B6%29%28x-3.5%29
.
You can always use the quadratic formula to find the factors:
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-8x%2B-21+=+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=%28-8%29%5E2-4%2A4%2A-21=400.

Discriminant d=400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+400+%29%29%2F2%5C4+=+3.5
x%5B2%5D+=+%28-%28-8%29-sqrt%28+400+%29%29%2F2%5C4+=+-1.5

Quadratic expression 4x%5E2%2B-8x%2B-21 can be factored:
4x%5E2%2B-8x%2B-21+=+4%28x-3.5%29%2A%28x--1.5%29
Again, the answer is: 3.5, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-8%2Ax%2B-21+%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You can also keep everything in the integers by expressing your factors as:



2 X 2 is 4; 3 X -7 is -21; and 2 X -7 + 2 X 3 is -8

John

My calculator said it, I believe it, that settles it

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Hello. I am having a problem factoring this equation and I am asking for your help. The equation is:
4x^2-8x-21
I tried multiplying -21x4 which = -84 , but I can't seem to find the 2 terms that make -8. Am I just confusing myself or is it staring me in the face? Please help me. 
You seem to be using the "ac" method, which means that you need 2 factors that when multiplied produce - 84,

and when summed, produce "b", or - 8 

These 2 factors are: highlight_green%28system%28-+14_and%2C_%2B+6%29%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
That's not an equation.
I can tell, there's no equal sign.