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 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

Answered by Henry N. Maths tutor

14677 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

If 3x+6x+3=21, find the value of x


What is completing the square?


f(x)=x^2+12x+32=0, solve for x


Solve 3x – 5 < 16


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences