SOLUTION: factor: x^2-13x-48

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Question 51432: factor: x^2-13x-48
Found 2 solutions by rchill, THANApHD:
Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-13x%2B-48+=+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=%28-13%29%5E2-4%2A1%2A-48=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+361+%29%29%2F2%5C1+=+16
x%5B2%5D+=+%28-%28-13%29-sqrt%28+361+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B-13x%2B-48 can be factored:
1x%5E2%2B-13x%2B-48+=+1%28x-16%29%2A%28x--3%29
Again, the answer is: 16, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-13%2Ax%2B-48+%29

Answer by THANApHD(104) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-13x-48
=x^2-16x+3x-48
=x(x-16)+3(x-16)
=(x+3)(x-16)