SOLUTION: i have to find the solution... 2x^2+6x+5=0 i have tried it with the completed square which means 2x^2+6x+9 = -5+9 at the end i was with (2x+3)(x+3)=4 no complete square... then

Algebra ->  Average -> SOLUTION: i have to find the solution... 2x^2+6x+5=0 i have tried it with the completed square which means 2x^2+6x+9 = -5+9 at the end i was with (2x+3)(x+3)=4 no complete square... then       Log On


   



Question 193042: i have to find the solution... 2x^2+6x+5=0
i have tried it with the completed square which means 2x^2+6x+9 = -5+9
at the end i was with (2x+3)(x+3)=4 no complete square...
then i tried to divide it by 2 so i had x^2 +3x+4.5=2
but with 4.5 i am not getting a complete square either...
Now i don't know any further... PLEASE help me!
Anna

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
i have to find the solution... 2x^2+6x+5=0
i have tried it with the completed square which means 2x^2+6x+9 = -5+9
at the end i was with (2x+3)(x+3)=4 no complete square...
then i tried to divide it by 2 so i had x^2 +3x+4.5=2
but with 4.5 i am not getting a complete square either...
-------------
Dividing by 2 is the best approach.
x^2 +3x+2.5=0 Start from here
x^2 + 3x + 2.25 = -0.25
(x + 1.5)^2 = -0.25
x+1.5 = +0.5i
x+1.5 = -0.5i
--------------
x = -3/2 + i/2
x = -3/2 - i/2
------------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B2.5+=+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=%283%29%5E2-4%2A1%2A2.5=-1.

The discriminant -1 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 -1 is + or - sqrt%28+1%29+=+1.

The solution is x%5B12%5D+=+%28-3%2B-i%2Asqrt%28+-1+%29%29%2F2%5C1+=++%28-3%2B-i%2A1%29%2F2%5C1+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B2.5+%29