SOLUTION: Solve this equation by completing the square. 3x^2 - 4x = -2

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Question 980552: Solve this equation by completing the square.
3x^2 - 4x = -2
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics
Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert to standard form by dividing both sides by 3:
We have: . What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of x is -1.33333333333333, we know that -1.33333333333333=2*somenumber, or . So, we know that our equation can be rewritten as , and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that is equivalent to our original equation .


The highlighted red part must be equal to 0.666666666666667 (highlighted green part).

, or .
So, the equation converts to , or .

Our equation converted to a square , equated to a number (-0.222222222222222).

There is no number whose square can be negative. So, there is no solution to this equation

Solved by pluggable solver: SOLVE quadratic equation with variable
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

Here's your graph:
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