SOLUTION: Could you show me how to factor by grouping? I have two problems I have been working on but do not understand how to get the final answers to the problems;1.21u^2-40u-21;2.5c^2+18c

Algebra ->  Equations -> SOLUTION: Could you show me how to factor by grouping? I have two problems I have been working on but do not understand how to get the final answers to the problems;1.21u^2-40u-21;2.5c^2+18c      Log On


   

Question 317458: Could you show me how to factor by grouping? I have two problems I have been working on but do not understand how to get the final answers to the problems;1.21u^2-40u-21;2.5c^2+18c-35
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
1.21u^2-40u-21
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation au%5E2%2Bbu%2Bc=0 (in our case 1.21u%5E2%2B-40u%2B-21+=+0) has the following solutons:

u%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=%28-40%29%5E2-4%2A1.21%2A-21=1701.64.

Discriminant d=1701.64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--40%2B-sqrt%28+1701.64+%29%29%2F2%5Ca.

u%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+1701.64+%29%29%2F2%5C1.21+=+33.5747683401831
u%5B2%5D+=+%28-%28-40%29-sqrt%28+1701.64+%29%29%2F2%5C1.21+=+-0.516917100513695

Quadratic expression 1.21u%5E2%2B-40u%2B-21 can be factored:
1.21u%5E2%2B-40u%2B-21+=+1.21%28u-33.5747683401831%29%2A%28u--0.516917100513695%29
Again, the answer is: 33.5747683401831, -0.516917100513695. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1.21%2Ax%5E2%2B-40%2Ax%2B-21+%29

5c^2+18c-35
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ac%5E2%2Bbc%2Bc=0 (in our case 5c%5E2%2B18c%2B-35+=+0) has the following solutons:

c%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=%2818%29%5E2-4%2A5%2A-35=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+1024+%29%29%2F2%5Ca.

c%5B1%5D+=+%28-%2818%29%2Bsqrt%28+1024+%29%29%2F2%5C5+=+1.4
c%5B2%5D+=+%28-%2818%29-sqrt%28+1024+%29%29%2F2%5C5+=+-5

Quadratic expression 5c%5E2%2B18c%2B-35 can be factored:
5c%5E2%2B18c%2B-35+=+5%28c-1.4%29%2A%28c--5%29
Again, the answer is: 1.4, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B18%2Ax%2B-35+%29