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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

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 - .

The solution is , or
Here's your graph:
Answer by Onmyoji.S(32)   (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
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