Factoring Quadratics Completing the Square

Solve the equation by factoring.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

• Set the equation equal to zero

• Divide 10 by 2 and add the result to both sides

• Add a² and 10a together

• Subtract the 21

What do you do to the b value to correctly complete the square?

• square it

• divide it by 2 and square the result

• divide it by 2 and take the square root of the result

• divide it by 2 only

Write the following quadratic expression in completed square form...

x² + 6x = 5

• (x + 3)² = 5

• (x + 6)² = 9

• (x + 3)² = 14

• (x + 6)² = 14

Solve by factoring: x² - 5x + 6 = 0
Put the solutions in order from least to greatest.

{​ (a)   ,​ (b)   }

• -6

• 3

• 6

• -3

• 9

• -2

• -9

• 2

• 18

• -1

Solve by factoring: x² + 3x - 18 = 0
Put the solutions in order from least to greatest.

{​ (a)   ,​ (b)   }

• -6

• 3

• 6

• -3

• 9

• -2

• -9

• 2

• 18

• -1

Solve by factoring: x² - 5x + 6 = 0
Put the solutions in order from least to greatest.

• -6

• 3

• 6

• -3

• 9

• -2

• -9

• 2

• 18

• -1

Solving the equation f(x) = x² - 8x + 15 =0, what are the two factors we can create to solve this equation? ​ (a)   .

• (x - 3) and (x - 5)

• (x + 3) and (x + 5)

• (x - 15)

A new high school gym is painting the gym floor to represents the boundaries of a volleyball court. The court is shaped like a rectangle and has an area of 162 meters. The length of the court is 9 meters greater than the width. The situation can be represented by the equation w2 + 9w- 162 = 0. What is the width of the volleyball court in meters?

Enter your answer in the space provided.

Mathematical Equivalence

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Solve the following quadratics equation by completing the square... x² - 10x - 5 = 0

• x = -5 ± √30

• x = 5 ± √30

• x = 30 ± √5

• x = -30 ± √5