How do I complete the square

Take a look at the expression below:

x+ 4x + 3

To complete the square you have to focus on the number before the x or the (x coefficient).

In this case, this number is 4.

To complete the square you take that number (x coefficent) and halve it, then square it.

Therefore: 4/2 = 2 -----> 2= 4

We then add this number after the x and also minus it after the last number (constant):

x+ 4x + 4 + 3 - 4

Completing the square is about being able to factorise, which is why this expression can now be factorised:

(x2 + 4x + 4) + 3 - 4

The brackets factorise to --> (x + 2)2 whilst the digits outside the brackets equate to -1

Therefore, our completed expression would now look like: (x + 2)2 - 1

The reason this is useful is because if our original expression was an equation it would look like this:

x+ 4x + 3 = 0

Therefore, our new equation would look like this:

(x+2)2 - 1 = 0

With our original equation the only way we could solve it is by using the quadratic formula.

But with our new factorised equation we can solve for x by quick algebra manipulation:

--> (x+2)2 - 1 = 0

--> (x+2)2 = 1

--> (x+2) = sqrt(1)

--> x + 2 = 1

--> x = 1 - 2

Therefore: x = -1

Answered by Anant M. Maths tutor

2351 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do i change a recurring decimal into a fraction?


There are 3 red beads and 1 blue bead in a jar. A bead is taken at random from the jar. what is the probability that the bead is blue?


Solve 3x + 6 > 3 - 2x.


Bhavin, Max and Imran share 6000 rupees in the ratios 2 : 3 : 7 Imran then gives 3/5 of his share of the money to Bhavin. What percentage of the 6000 rupees does Bhavin now have? Give your answer correct to the nearest whole number.


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