SOLUTION: Solve 16 + 3 =5 ___________ ____ x+5 x-2

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Question 551791: Solve 16 + 3 =5
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x+5 x-2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve 16 + 3 =5
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x+5 x-2
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You're going to some trouble just to make things confusing.
I think you mean:
16%2F%28x%2B5%29+%2B+3%2F%28x-2%29+=+5
Multiply thru by (x+5)*(x-2)
16%28x-2%29+%2B+3%28x%2B5%29+=+5%28x%2B5%29%28x-2%29+=+5x%5E2+%2B+15x+-+50
19x+-+17+=+5x%5E2+%2B+15x+-+50
5x%5E2+-+4x+-+33+=+0
Can you finish it?
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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 5x%5E2%2B-4x%2B-33+=+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=%28-4%29%5E2-4%2A5%2A-33=676.

Discriminant d=676 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+676+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+676+%29%29%2F2%5C5+=+3
x%5B2%5D+=+%28-%28-4%29-sqrt%28+676+%29%29%2F2%5C5+=+-2.2

Quadratic expression 5x%5E2%2B-4x%2B-33 can be factored:
5x%5E2%2B-4x%2B-33+=+%28x-3%29%2A%28x--2.2%29
Again, the answer is: 3, -2.2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-4%2Ax%2B-33+%29

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x = -2.2, x = 3