# Completing the square

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##### Introduction
###### Lessons
1. What is "COMPLETING THE SQUARE"?
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##### Examples
###### Lessons
1. Recognizing a Polynomial that Can Be Written as a Perfect Square
Convert the following expressions into perfect squares, if possible:
1. ${x^2} + 6x + {3^2}$ =
${x^2} - 6x + {\left( { - 3} \right)^2}$ =
2. ${x^2} + 20x + 100$ =
${x^2} - 20x + 100$ =
${x^2} - 20x - 100$ =
2. Completing the Square
Add a constant to each quadratic expression to make it a perfect square.
1. ${x^2} + 10x + \;$_____ =
2. ${x^2} - 2x + \;$_____ =
3. $2{x^2} + 12x + \;$_____ =
4. $- 3{x^2} + 60x + \;$_____ =
5. $\frac{2}{5}{x^2} - 8x + \;$_____ =
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###### Topic Notes
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