Question

write the function f(x) = 2x 2 + 7x + 6 in completed square form.

Answer 1

Answer:

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=+1/4Finally subtracting 7/4 leaves us with our answer:

9) x=3/2 or x=2

Step-by-step explanation: