Completing the Square in Math
Examples & Formula for completing the square
The process for finding the last term of a perfect square trinomial is called completing the square
Formula for Completing the Square
First off, a little necessary voculabulary:
a perfect square trinomial is a polynomial that you get by squareing a binomial.(binomials are things like 'x + 3' or 'x − 5')
Examples of perfect square trinomials (the red trinomials)
- (x+ 1)² = x² + 2x + 1
- (x+ 2)² = x² + 4x + 4
- (x+ 3)² = x² + 6x + 9
Examples of trinomials that are NOT perfect square trinomials
- (x+ 1)(x +2)= x² + 3x + 2
- (x+ 2)(x+5) = x² + 7x + 10
- (x+ 3)(x −3)= x² − 9
To best understand the formula and logic behind completing the square, look at each example below and you should see the pattern that occurs whenever you square a binomial to produce a perfect square trinomial.
As the examples above show, the square of a binomial always follows the same pattern and formula.
Given a quadratic equation x² + bx + c that is a SQUARE OF A BINOMIAL
c is always the square of ½(b)
ie c = ½(b)²
Make sure that you understand the rule stated above that c is the squre of half of b only is true for perfect square trinomials
. It does not apply to other trinomials.
Practice Completing the Square