The process for finding the last term of a perfect square trinomial is called 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
1. Solve the quadratic equation below by completing the square:
Equation: x²+ 16x = 36
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2. Complete the square to solve the quadratic equation below.
Equation: x² + 10x = 24
3. Find the solutions of the quadratic equation below by completing its square.
x² + 24x = 25
4. Find the solutions of the quadratic equation below by completing its square.
x² + 8x = −20
4. Complete the square of the quadratic equation below to find its solution(s)
x² + 8x = −20
5. Complete the square of the quadratic equation below to find its solution(s)
x² + 18x + 90= 0
6. Complete the square of the quadratic equation below to find its solution(s)
x² − 4x − 12= 0
