SOLUTION: Find the value of d such that u2-12u+d

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Question 146424: Find the value of d such that

u2-12u+d
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean u%5E2-12u%2Bd+=+0?
If so,
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-12x%2B1+=+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=%28-12%29%5E2-4%2A1%2A1=140.

Discriminant d=140 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+140+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+140+%29%29%2F2%5C1+=+11.9160797830996
x%5B2%5D+=+%28-%28-12%29-sqrt%28+140+%29%29%2F2%5C1+=+0.0839202169003839

Quadratic expression 1x%5E2%2B-12x%2B1 can be factored:
1x%5E2%2B-12x%2B1+=+%28x-11.9160797830996%29%2A%28x-0.0839202169003839%29
Again, the answer is: 11.9160797830996, 0.0839202169003839. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B1+%29

There are 2 real roots, 6+%2B+sqrt%2835%29, and
6+-+sqrt%2835%29
The online solution always uses x, just substitute u for it.