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
