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

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

All quadratic equations take the general form:

ax²+bx+c=0

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 3 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

Therefore:

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

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