SOLUTION: find the type and number of solutions for each equation 2x^-16x=-32 3x^2-8x+8=0

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Question 559999: find the type and number of solutions for each equation
2x^-16x=-32
3x^2-8x+8=0

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the type and number of solutions for each equation
2x%5E-16x=-32
x%5E-15+=+-16
16x%5E15+=+-1
x+=+root%2815%2C%28-1%2F16%29%29
x =~ -0.8312
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3x%5E2-8x%2B8=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-8x%2B8+=+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%2A3%2A8=-32.

The discriminant -32 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 -32 is + or - sqrt%28+32%29+=+5.65685424949238.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-8%2Ax%2B8+%29