SOLUTION: Can someone help clear up something for me? Are complex numbers the same as complex solutions? I've been trying solve the problem using quardratic formula, but I don't come anywhe

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Can someone help clear up something for me? Are complex numbers the same as complex solutions? I've been trying solve the problem using quardratic formula, but I don't come anywhe      Log On


   

Question 447580: Can someone help clear up something for me?
Are complex numbers the same as complex solutions? I've been trying solve the problem using quardratic formula, but I don't come anywhere close.
x^2+37=0
Thanks
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A number is just a number, whether it's real or complex.
Any number can be a solution to some equation.
x%5E2+%2B+37+=+0
x+=+sqrt%28-37%29+=+i%2Asqrt%2837%29
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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%2B0x%2B37+=+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=%280%29%5E2-4%2A1%2A37=-148.

The discriminant -148 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 -148 is + or - sqrt%28+148%29+=+12.1655250605964.

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%2B0%2Ax%2B37+%29