SOLUTION: Find the roots of the quadratic equation x2 − 18x + 18 = 0 .

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Question 272571: Find the roots of the quadratic equation x2 − 18x + 18 = 0 .
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - 18x + 18 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-18x%2B18+=+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%2A18=252.

Discriminant d=252 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18%2B-sqrt%28+252+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+252+%29%29%2F2%5C1+=+16.9372539331938
x%5B2%5D+=+%28-%28-18%29-sqrt%28+252+%29%29%2F2%5C1+=+1.06274606680623

Quadratic expression 1x%5E2%2B-18x%2B18 can be factored:
1x%5E2%2B-18x%2B18+=+1%28x-16.9372539331938%29%2A%28x-1.06274606680623%29
Again, the answer is: 16.9372539331938, 1.06274606680623. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18%2Ax%2B18+%29