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
WARNING:
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
problem 4) Find the solutions of the quadratic equation below by completing its square.
x² + 8x = −20
problem 5) Complete the square of the quadratic equation below to find its solution(s)
x² + 8x = −20
problem 6) Complete the square of the quadratic equation below to find its solution(s)
x² + 18x + 90= 0
problem 7 ) Complete the square of the quadratic equation below to find its solution(s)
x² − 4x − 12= 0
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Completing the Square Worksheet(25 question pdf with answer key)
Graphing Calc
