SOLUTION: If someone could please help me with this, it will be a huge help. 1) Solve -16t^2 -8t = 10 by completing the square.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If someone could please help me with this, it will be a huge help. 1) Solve -16t^2 -8t = 10 by completing the square.       Log On


   

Question 1029212: If someone could please help me with this, it will be a huge help.

1) Solve -16t^2 -8t = 10 by completing the square.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve -16t^2 -8t = 10 by completing the square.
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16t^2 + 8t = -10
t^2 + (1/2)t = -5/8
c = (b/2a)^2 = (8/32)^2 = 1/16
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t^2 + (1/2)t + 1/16 = -5/8 + 1/16 = -9/16
(t+1/4)^2 = -9/16
t + 1/4 = ± sqrt(-9/16) = ±3i/4
t = -1/4 ± 3i/4
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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 -16x%5E2%2B-8x%2B-10+=+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%2A-16%2A-10=-576.

The discriminant -576 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -576 is + or - sqrt%28+576%29+=+24.

The solution is x%5B12%5D+=+%28--8%2B-i%2Asqrt%28+-576+%29%29%2F2%5C-16+=++%28--8%2B-i%2A24%29%2F2%5C-16+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B-8%2Ax%2B-10+%29