SOLUTION: I could really use some help on this equation: Consider the equation 5x^2 + 5 = 8x. Find the complex solutions (real and non-real) of the equation, and simplify as much as poss

Algebra ->  Graphs -> SOLUTION: I could really use some help on this equation: Consider the equation 5x^2 + 5 = 8x. Find the complex solutions (real and non-real) of the equation, and simplify as much as poss      Log On


   

Question 1039081: I could really use some help on this equation:
Consider the equation 5x^2 + 5 = 8x. Find the complex solutions (real and non-real) of the equation, and simplify as much as possible. Show work please.
I really appreciate your help!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
5x^2 + 5 = 8x
5x^2 - 8x + 5 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-8x%2B5+=+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%2A5%2A5=-36.

The discriminant -36 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 -36 is + or - sqrt%28+36%29+=+6.

The solution is x%5B12%5D+=+%28--8%2B-i%2Asqrt%28+-36+%29%29%2F2%5C5+=++%28--8%2B-i%2A6%29%2F2%5C5+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-8%2Ax%2B5+%29