CP - Lesson: Solve Quad by Comp the Square

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Solve Quadratic Equations by Completing the Square

Objective: Solve quadratic equations by completing the square.​

Multiple Choice

(x + 3)² = ?

• x² + 6x + 9

• x² + 9

• x² + 3x + 9

• x² + 3x + 6

ANSWER

(x + 3)² = (x + 3)(x + 3)

= x² + 3x + 3x + 9

= x² + 6x + 9

Perfect Square Trinomial

PERFECT SQUARES TRINOMIALS

​Factor: x² - 10x + 25

​Factor: x² + 18x + 81

Questions to Ask
1) Are the 1st and 3rd term perfect squares?
2) If YES, multiply them and double it. Is that the middle term?

​Factor: x² - 20x + 100

Match

Match the following Quadratic with their factored form

• x² + 10x + 25

• x² + 16x + 64

• x² + 8x + 16

• x² + 12x + 36

• x² + 14x + 49

(x + 5)²

(x + 8)²

(x + 4)²

(x + 6)²

(x + 7)²

• (x + 5)²

• (x + 8)²

• (x + 4)²

• (x + 6)²

• (x + 7)²

Solve by Completing the Square

x² + 10x = -9

Perfect Square Trinomials
x² + 2x + 1 = (x + 1)²
x² + 4x + 4 = (x + 2)²
x² + 6x + 9 = (x + 3)²
x² + 8x + 16 = (x + 4)²
x² + 10x + 25 = (x + 5)²
x² + 12x + 36 = (x + 6)²
x² + 14x + 49 = (x + 7)²
x² + 16x + 64 = (x + 8)²
x² + 18x + 81 = (x + 9)²
x² + 20x + 100 = (x + 10)²

Math Response

Solve: x² + 14x = 51

(just give the NEGATIVE answer)

Type answer here

Correct Answer: -17

Deg^°

Rad

Solve by Completing the Square

x² - 12x = -11

Perfect Square Trinomials
x² + 2x + 1 = (x + 1)²
x² + 4x + 4 = (x + 2)²
x² + 6x + 9 = (x + 3)²
x² + 8x + 16 = (x + 4)²
x² + 10x + 25 = (x + 5)²
x² + 12x + 36 = (x + 6)²
x² + 14x + 49 = (x + 7)²
x² + 16x + 64 = (x + 8)²
x² + 18x + 81 = (x + 9)²
x² + 20x + 100 = (x + 10)²

Math Response

Solve: x² - 2x = 3

(just give the POSITIVE answer)

Type answer here

Correct Answer: 3

Deg^°

Rad

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