SOLUTION: x(squared)-18x-40=0

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Question 70804: x(squared)-18x-40=0
Answer by jim_thompson5910(35256) 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-18x%2B-40+=+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=%28-18%29%5E2-4%2A1%2A-40=484.

Discriminant d=484 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18%2B-sqrt%28+484+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+484+%29%29%2F2%5C1+=+20
x%5B2%5D+=+%28-%28-18%29-sqrt%28+484+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B-18x%2B-40 can be factored:
1x%5E2%2B-18x%2B-40+=+1%28x-20%29%2A%28x--2%29
Again, the answer is: 20, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18%2Ax%2B-40+%29

Remember this is only one branch of the quadratic and it is not a straight line (the other x-intercept is at x=20).