Algebra II 5-7 Completing the Square

𝑥 2 +𝑏𝑥+ 𝑏 2 2 = 𝑥+ 𝑏 2 2 𝑥 2 +6𝑥+9 YES 𝑥+3 2 𝑥 2 +10𝑥+100 NO

Solve 𝑥 2 +6𝑥+9=1 𝑥+3 2 =1 𝑥+3 2 = 1 𝑥+3=±1 𝑥=−2 𝑜𝑟 −4 𝑥 2 −2𝑥+1=4 𝑥−1 2 =4 𝑥−1=±2 𝑥=−1 𝑜𝑟 3

𝑥 2 +4𝑥−4=0 Move the 4 to the other side 𝑥 2 +4𝑥=4 Using Completing the square 𝑥 2 +4𝑥+4=4+4 ADD 𝑏 2 2 to both sides 𝑥+2 2 =8 Solve −2±2 2

𝑥 2 −2𝑥−1=0 𝑥 2 −2𝑥=1 𝑥 2 −2𝑥+1=1+1 𝑥−1 2 =2 𝑥−1=± 2 𝑥=1± 2

𝑥 2 +6𝑥+34=0 𝑥 2 +6𝑥=−34 𝑥 2 +6𝑥+9=−34+9 𝑥+3 2 =−25 𝑥+3= −25 𝑥+3=±5𝑖 𝑥=−3±5𝑖

2 𝑥 2 +𝑥=6 Divide the whole equation by 2 𝑥 2 + 1 2 𝑥=3 𝑥 2 + 1 2 𝑥+ 1 16 =3+ 1 16 𝑥+ 1 4 2 = 49 16 𝑥+ 1 4 =± 7 4 𝑥= 3 2 𝑜𝑟 −2

iRAT 𝑥 2 −3𝑥=28 𝑥 2 +6𝑥+41=0 𝑥 2 +4=0

Problems Page 285 #2-26 even