Completing the Square

​Review:

​Direction: Find the factors in each quadratic equations.

​Warm-up/Activity

​The following slides has a sentences that are incomplete and you have to fill in the blanks that makes a sentence.

Open Ended

After I finished my high school, I want to become _____________.

Open Ended

I spent my weekends __________.

Open Ended

My hobbies is/are ___________.

Open Ended

I love Mathematics because _______________.

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The weather today is ______________________.

Completing the Square

by JadeAnthony Dosdos

​Core Concepts:

Completing the square defines writing a quadratic in the form of a squared bracket and adding a constant.​

​Steps:

​1. Locate the coefficient of x.

​2. Then divide by 2.

​3. Squared the result.

​4. Add the result in both sides.

​5. Squared on the right sides.

​6. Then, simplify.

​Example:

​Solve x² + 10x = -9 by completing the square.

​1. Locate the coefficient of x.

​2. Then divide by 2.

​3. Squared the result.

​4. Add the result in both sides.

​5. Squared on the right sides.

​6. Then, simplify.

​Solution:

b = 10 ​

​

​x² + 10x + ___ = -9

​x² + 10x + 25 = -9 + 25

​x² + 10x + 25 = 16

​ (x+5)² = 16

​

​

​ (x+5)² = 4

​x = -1 and x = -9

​Example:

​Solve by completing the square.

​1. Locate the coefficient of x.

​2. Then divide by 2.

​3. Squared the result.

​4. Add the result in both sides.

​5. Squared on the right sides.

​6. Then, simplify.

​Solution:

​

​b = 14

​

​x² + 14x + ___ = 0 + 15

​x² + 14x + ___ = 15

​x² + 14x + 49 = 15 + 49

​ (x+7)² = 64

​

​ (x+7)² = 8

​ x = 1 and x = -15

Multiple Choice

Solve $$x^2-18x=40$$  by completing the square.

• x=20

  x=2

• x=-20

  x=2

• x=20

  x=-2

• x=-20

  x=-2

Multiple Choice

Solve  $$x^2+14x-51=0$$  by completing the square.

• x=3

  x=-17

• x=-3

  x=17

• x=3

  x=17

• x=-3

  x=-17