SOLUTION: 13x^2+14x+13=0

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Question 443940: 13x^2+14x+13=0
Found 2 solutions by chriswen, solver91311:
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 13x%5E2%2B14x%2B13+=+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=%2814%29%5E2-4%2A13%2A13=-480.

The discriminant -480 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 -480 is + or - sqrt%28+480%29+=+21.9089023002066.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+13%2Ax%5E2%2B14%2Ax%2B13+%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let me open by saying there is absolutely nothing wrong with the other tutor's answer. However, allow me to give you an alternate way to look at how you present your answer.



But then recognizing that 480 is equal to 16 times 30, we can write:



and



which are the simplified exact answers as contrasted with the numerical approximations given.


John

My calculator said it, I believe it, that settles it
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