SOLUTION: What are the solutions? 1/2x^2 + 2x + 3 =0

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Question 683655: What are the solutions?
1/2x^2 + 2x + 3 =0

Found 2 solutions by Alan3354, Onmyoji.S:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!

1/2x^2 + 2x + 3 =0
x^2 + 4x + 6 =0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B6+=+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=%284%29%5E2-4%2A1%2A6=-8.

The discriminant -8 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 -8 is + or - sqrt%28+8%29+=+2.82842712474619.

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%2B4%2Ax%2B6+%29


Answer by Onmyoji.S(32) About Me  (Show Source):
You can put this solution on YOUR website!
1/2x²+2x+3=0
2(1/2x²+2x+3)=0*2
x²+4x+6=0
x²+4x=-6 【(4/2)²=4】
x²+4x+4=-6+4 【completing the square】
(x+2)*(x+2) =-2
(x+2)² =-2
x=(+√-2)-2
x=(-√-2)-2