SOLUTION: X to the power of 3 or cubed + 216 = 0 ::::: we factor out (x+6) and are left with (x squared -6x + 36) ::: we know the answer is 3 plus or minus 3(times square root of 3i) but

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: X to the power of 3 or cubed + 216 = 0 ::::: we factor out (x+6) and are left with (x squared -6x + 36) ::: we know the answer is 3 plus or minus 3(times square root of 3i) but       Log On


   

Question 218953: X to the power of 3 or cubed + 216 = 0 ::::: we factor out (x+6) and are left with (x squared -6x + 36) ::: we know the answer is 3 plus or minus 3(times square root of 3i) but can't get there :::
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
X to the power of 3 or cubed + 216 = 0 ::::: we factor out (x+6) and are left with (x squared -6x + 36) ::: we know the answer is 3 plus or minus 3(times square root of 3i) but can't get there :::
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x%5E3+%2B+216+=+0
%28x%2B6%29%2A%28x%5E2+-+6x+%2B+36%29+=+0
x = -6
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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-6x%2B36+=+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=%28-6%29%5E2-4%2A1%2A36=-108.

The discriminant -108 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 -108 is + or - sqrt%28+108%29+=+10.3923048454133.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B36+%29