How can I complete the square?

HOW CAN I...?

Complete the square for the following equation Let’s write the expression in standard form

x2 − 16x + 99 − 10 = 0 x2 − 16x + 89 = 0 2 ax + bx + c b −16 = −8 = 2 2 b 2 (2) =

2=

(−8)

64

x2 − 16x + 89 = 0 We are going to add and subtract b 2 (2)

→ 64 x2 − 16x + 64 − 64 + 89 = 0 Grouping (x2 − 16x + 64) − 64 + 89 = 0 (x−)(x−) +25 (x − 8)(x − 8) +25= 0 2 (x − 8) = −25

Complete the square for the following expression

Same idea: write in standard form −6x2 + 64x + 8x − 222 = 0 −6x2 + 72x − 222 = 0 Divide by -6 to have coefficient 1 −6x2 + 72x − 222 = 0 −6

−6

−6

−6

x2 − 12x + 37 = 0

Now the same process

b 2 (2) =

−12 2 ( 2 )

(−6)2 = 36 add and subtract 36 2

x − 12x + 36 − 36 + 37 = 0 2

(x − 12x + 36) + 1 = 0 (x−)(x−) = −1 (x − 6)(x − 6) = −1 (x − 6)2 = −1