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 1 2 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 + 1 2 ∗ 3 2 2 + 1 2 ∗ 3 2 2 𝑥 2 − 3 2 𝑥+ 3 4 2 =1+ 3 4 2 𝒙− 𝟑 𝟒 𝟐 =1+ 9 16 = 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

Divide both sides by coefficient of x2 Left side -- 𝑥2+𝑏𝑥 Add 1 2 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 2 + 2 3 𝑥− 7 12 =0 + 7 12 + 7 12 𝑥 2 + 2 3 𝑥 = 7 12 + 1 2 ∗ 2 3 2 + 1 2 ∗ 2 3 2 𝑥 2 + 2 3 𝑥+ 1 3 2 = 7 12 + 1 3 2 𝒙+ 𝟏 𝟑 𝟐 = 7 12 + 1 9 = 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

Divide both sides by coefficient of x2 Left side -- 𝑥2+𝑏𝑥 Add 1 2 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 2 + 19 5 𝑥− 66 5 =0 + 66 5 + 66 5 𝑥 2 + 19 5 𝑥 = 66 5 + 1 2 ∗ 19 5 2 + 1 2 ∗ 19 5 2 𝑥 2 + 19 5 𝑥+ 19 10 2 = 66 5 + 19 10 2 𝒙+ 𝟏𝟗 𝟏𝟎 𝟐 = 66 5 + 361 100 = 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