SOLUTION: Use the equation x2-8x=-9 circle one of the following: real imaginary circle one of the following: rational irrational circle one of the following: equal unequal

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Question 975038: Use the equation x2-8x=-9
circle one of the following: real imaginary
circle one of the following: rational irrational
circle one of the following: equal unequal
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x2-8x=-9
x%5E2+-+8x+%2B+9+=+0
Disc = b^2 - 4ac = 8^2 - 36
Disc > 0 --> 2 real roots.
Disc = 28, sqrt(28) is irrational
--> irrational
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B9+=+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=%28-8%29%5E2-4%2A1%2A9=28.

Discriminant d=28 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+28+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+28+%29%29%2F2%5C1+=+6.64575131106459
x%5B2%5D+=+%28-%28-8%29-sqrt%28+28+%29%29%2F2%5C1+=+1.35424868893541

Quadratic expression 1x%5E2%2B-8x%2B9 can be factored:
1x%5E2%2B-8x%2B9+=+%28x-6.64575131106459%29%2A%28x-1.35424868893541%29
Again, the answer is: 6.64575131106459, 1.35424868893541. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B9+%29