1. Get out your binders! Today’s Objectives:
You will be able to solve quadratics by completing the square
Today’s Objectives:

2. Warm Up Solve each equation by using the Square Root Property.
𝑥 2 +4𝑥+4=25
𝑥 2 −14𝑥+49=20
Find the value of 𝒄 that makes a perfect square. Then write the trinomial as a perfect square.
𝑥 2 +5𝑥+𝑐
𝑥 2 +10𝑥+𝑐

3. 4.5 Completing the Square
All quadratic equations that can be solved using the Completing the Square Method.
This is done by manipulating the equation until the LEFT side is a perfect square and then using the Square Root Method.

4. Completing the Square
𝒙 𝟐 +𝟏𝟔𝒙=𝟗
𝑥+8=± 73
− −8
𝒙=−𝟖± 𝟕𝟑

5. Solve by Completing the Square. 𝑥 2 +10=11 2 𝑥 2 −7𝑥+5=0 𝑥 2 +8𝑥+22=0
Examples
Solve by Completing the Square.
𝑥 2 +10=11
2 𝑥 2 −7𝑥+5=0
𝑥 2 +8𝑥+22=0

6. Examples Solve by Completing the Square. 𝑥 2 −10𝑥+24=0 3 𝑥 2 +14𝑥−16=0
𝑥 2 −6𝑥+25=0

7. You Try! Solve by Completing the Square. 𝑥 2 +10𝑥+9=0 3 𝑥 2 +10𝑥−8=0
𝑥 2 +2𝑥+2=0

8. Solve by Completing the Square. 𝑥 2 −4𝑥+12=0 𝑥 2 +2𝑥−12=0 𝑥 2 −4𝑥+3=0
More Examples
Solve by Completing the Square.
𝑥 2 −4𝑥+12=0
𝑥 2 +2𝑥−12=0
𝑥 2 −4𝑥+3=0

9. Homework
Lesson 4.5
Pg. 260 #8-13, 30-32