# Completing the square

### Completing the square

#### Lessons

perfect squares:
• ${\left( {x + a} \right)^2} = {x^2} + 2ax + {a^2}$
• ${\left( {x - a} \right)^2} = {x^2} - 2ax + {a^2}$
• completing the square: adding a constant to a quadratic expression to make it a perfect square
• Introduction
What is “COMPLETING THE SQUARE”?
a)
Review: expanding a perfect square.

b)
How to convert a polynomial into a perfect square

c)
How to complete the square

• 1.
Recognizing a Polynomial that Can Be Written as a Perfect Square
Convert the following expressions into perfect squares, if possible:
a)
${x^2} + 6x + {3^2}$ =
${x^2} - 6x + {\left( { - 3} \right)^2}$ =

b)
${x^2} + 20x + 100$ =
${x^2} - 20x + 100$ =
${x^2} - 20x - 100$ =

• 2.
Completing the Square
Add a constant to each quadratic expression to make it a perfect square.
a)
${x^2} + 10x + \;$_____ =

b)
${x^2} - 2x + \;$_____ =

c)
$2{x^2} + 12x + \;$_____ =

d)
$- 3{x^2} + 60x + \;$_____ =

e)
$\frac{2}{5}{x^2} - 8x + \;$_____ =