Solve the quadratic 2x^2+7x+6 by completing the square

All quadratic equations take the general form:


The first step used to comlete the square is to divide the whole equation by the a term, in our case 2:

1)        x2+(7/2)x+3=0

We then move our c term to the right hand side of the equation by subtracting from both sides:

2)        x2+(7/2)x=_3

Let us, for a moment, just examine the left hand side of this equation. We can see that:

3)        (x+7/4)2=x2+(7/2)x+(7/4)2


4)         x2+(7/2)x=(x+7/4)2-(7/4)2

Inserting equation 4 into equation 2 gives:

5)        (x+7/4)2-(7/4)2=_3

We can re-arrange to get:

6)        (x+7/4)2=_3+(7/4)2

Simplifying the right hand side gives:

7)        (x+7/4)2=1/16

Taking the square root of both sides gives(baring in mind that taking the square root of a number gives us a positive and a negative number):

8)        x+7/4=+1/4

Finally subtracting 7/4 leaves us with our answer:

9)        x=_3/2 or x=_2

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