1. Solving Quadratics by Completing the Square
9.4 Day 1
Solving Quadratics by Completing the Square

2. Warm-Up
Factor the following: 1. 𝑥 2 +20𝑥 𝑥 2 −18𝑥 𝑥 2 −4𝑥+4

3. Completing the Square
Steps to solving a quadratic equation by completing the square:
1. Get the equation in the form 𝑎𝑥 2 +𝑏𝑥 ______=𝑐 ______.
(Move the c value to the other side, leaving blanks as shown above) 
2. To fill in the blanks: Divide the b value by and ____________ it.
the perfect square trinomial
the equation for x using square roots

4. Example 1
a) Find the value of c that makes x2 – 12x + c a perfect square trinomial.
b) Find the value of c that makes x2 + 14x + c a perfect square trinomial.

5. Example 2
Solve the quadratic equations using completing the square. A. 𝑥 2 +10𝑥−3=0 B. 𝑥 2 −6𝑥−8=0

6. Example 2 cont.
C. 𝑥 2 +6𝑥+5=12

7. If the Coefficient is not 1….
If the coefficient of x2 is not 1…we have to do one extra step!
FIRST: each side of the equation by the of x2

8. Example 3
a) 3x2 – 6x – 12 = 0 b) 5x2 – 10x + 30 = 0

9. Example 3 cont.
c) –2x2 + 36x – 10 = 24