SOLUTION: (t-2)^2=-16 solve the equation

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Question 233658: (t-2)^2=-16 solve the equation
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(t-2)^2=-16
t-2 = sqrt(-16) = ±4i
t = 2 + 4i
t = 2 - 4i
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t%5E2+-+4t+%2B+20+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation a0%5E2%2Bb0%2Bc=0 (in our case 10%5E2%2B-40%2B20+=+0) has the following solutons:

0%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%2A1%2A20=-64.

The discriminant -64 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 -64 is + or - sqrt%28+64%29+=+8.

The solution is 0%5B12%5D+=+%28--4%2B-+i%2Asqrt%28+-64+%29%29%2F2%5C1+=++%28--4%2B-+i%2A8%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B20+%29

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I don't know why the solver multiplied by 10, but the results are the same.