1. Completing the Square 8 𝑥 2 −12𝑥−8=0 8 8 8 8
Divide both sides by coefficient of x2
Left side -- 𝑥2+𝑏𝑥
Add 𝑏 2 to both sides
Factor Left Side
Simplify Right Side
Solve for x
𝑥 2 − 3 2 𝑥−1=0 +1 +1
𝑥 2 − 3 2 𝑥 =1
∗ ∗
𝑥 2 − 3 2 𝑥 =
𝒙− 𝟑 𝟒 𝟐 =
= 𝟐𝟓 𝟏𝟔
𝒙− 𝟑 𝟒 𝟐 =± 𝟐𝟓 𝟏𝟔
→ 𝒙− 𝟑 𝟒 𝟐 = 𝟐𝟓 𝟏𝟔 →
𝒙− 𝟑 𝟒 =± 𝟓 𝟒
𝒙= 𝟑 𝟒 ± 𝟓 𝟒
→𝒙= 𝟑 𝟒 + 𝟓 𝟒 , 𝟑 𝟒 − 𝟓 𝟒
𝑥=2, − 1 2

2. Divide both sides by coefficient of x2
Left side -- 𝑥2+𝑏𝑥
Add 𝑏 2 to both sides
Factor Left Side
Simplify Right Side
Solve for x
24 𝑥 2 +16𝑥−14=0 24 24 24 24
𝑥 𝑥− 7 12 =0
+ 7 12
+ 7 12
𝑥 𝑥 = 7 12
∗ ∗
𝑥 𝑥 =
𝒙+ 𝟏 𝟑 𝟐 =
= 𝟐𝟓 𝟑𝟔
𝒙+ 𝟏 𝟑 𝟐 =± 𝟐𝟓 𝟑𝟔
→𝒙+ 𝟏 𝟑 =± 𝟓 𝟔
→𝒙=− 𝟏 𝟑 + 𝟓 𝟔 ,− 𝟏 𝟑 − 𝟓 𝟔
𝑥= 1 2 , − 7 6

3. Divide both sides by coefficient of x2
Left side -- 𝑥2+𝑏𝑥
Add 𝑏 2 to both sides
Factor Left Side
Simplify Right Side
Solve for x
5 𝑥 2 +19𝑥−66=0 5 5 5 5
𝑥 𝑥− 66 5 =0
+ 66 5
+ 66 5
𝑥 𝑥 = 66 5
∗ ∗
𝑥 𝑥 =
𝒙+ 𝟏𝟗 𝟏𝟎 𝟐 =
= 𝟏𝟔𝟖𝟏 𝟏𝟎𝟎
𝒙+ 𝟏𝟗 𝟏𝟎 𝟐 =± 𝟏𝟔𝟖𝟏 𝟏𝟎𝟎
𝒙+ 𝟏𝟗 𝟏𝟎 𝟐 = 𝟏𝟔𝟖𝟏 𝟏𝟎𝟎
𝒙+ 𝟏𝟗 𝟏𝟎 =± 𝟒𝟏 𝟏𝟎
𝒙=− 𝟏𝟗 𝟏𝟎 + 𝟒𝟏 𝟏𝟎 ,− 𝟏𝟗 𝟏𝟎 − 𝟒𝟏 𝟏𝟎
𝑥= 11 5 , −6