Solving Quadratic Equations by Completing The Square

​Solving Quadratic Equations by Completing The Square

​Objective:

• Solve quadratic equations by completing the square

Poll

Knowledge Rating Chart

Choose the number that represents your learning experience on completing the square.

• I've never heard of this before.

• I've heard of this, but I'm not sure how it works.

• I know about this and how to use it

​Exploration: Consider the figure below.

​1. Find the areas of:

A = ____

B = ____

C = ____

​Exploration: Consider the figure below.

​1. Find the areas of:

A = x²

B = 6x

C = 6x

​Exploration: Consider the figure below.

​2. Complete the big square by adding a figure.

​Exploration: Consider the figure below.

​3. What is the area of D?

4. What is the area of the big square?

5. Give the dimensions of the big square,​

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​

​Exploration: Consider the figure below.

​3. What is the area of D? 36

4. What is the area of the big square? x² + 12x + 36

5. Give the dimensions of the big square. (x + 6) (x + 6)

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​Completing the square

​Example 1. Complete the square of x² + 14x _____. Then write it in factored form.

​Example 2. Complete the square of x² - 5x _____. Then write it in factored form.

Multiple Choice

Complete the square.

$$x^2\ -3x$$  

• $$x^2-3x\ +\ \frac{9}{4}$$  

• $$x^2-3x-\frac{9}{4}$$  

• $$x^2-3x+9$$  

• $$x^2-3x^2-9$$  

Multiple Choice

What expression must be added to x² + 10x to make it a perfect square trinomial?

• 5

• 25

• 100

Multiple Choice

What is the factored form of x² + 18x + 81?

• (x + 9)²

• (x - 9)²

• (x + 6)²

• (x - 6)²

​Example 3. Solve x² + 8x + 2 = 0 by completing the square.

​Example 4. Solve x² - 5x + 6 = 0 by completing the square.

​Example 4. Solve x² - 5x + 6 = 0 by completing the square.

Draw

Solve by completing the square.

x² - 2x - 12 = 0

​Worktext reference

​Oronce O.A., Mendoza M.O. (2019). E-Math Worktext in Mathematics 9, Manila, Philippines: REX Bookstore Inc.

Nivera G.C., Lapinid M.R.C. (2018). Grade 9 Mathematics Patterns and Practicalities 9, Makati City, Philippines: Salesiana Books by Don Bosco Press, Inc.

Reference