Thread: Completing the square and simplifying.

Can you please help me and solve these questions by completing the square (keeping the fractions in fraction-form rather than changing them to decimals) and can you please show your work, so I can see what you're
doing? Also, can you then simplify the fractions? If you cannot do all of them, can you do at least one? PLEASE. I'm really confused.

1.) 2/3^2 - 2x - 3 = 0
2.) 1/4n^2 + n = - 1/8
3.) 3m^2 + 8m + 8 = 0

Use the quatratic formula.

If

Then:
http://trevorpythag.files.wordpress..../02/qdrtc2.gif

1.) 2/3^2 - 2x - 3 = 0
2.) 1/4n^2 + n = - 1/8
3.) 3m^2 + 8m + 8 = 0

3) Solution: 3m^2 + 8m + 8 = 0,

3m^2 + 8m = -8

m^2 + (8/3)m = -8/3, complete the square,

m^2 + (8/3)m + ((8/3)/2)^2 = -8/3 + ((8/3)/2)^2,

m^2 + (8/3)m + (8/6)^2 = -8/3 + (8/6)^2,

m^2 + (8/3)m + (4/3)^2 = -8/3 + (4/3)^2,

(m + 4/3)^2 = -8/3 + 16/9,

(m + 4/3)^2 = (-24 + 16)/9,

(m + 4/3)^2 = -8/9, take square root of BS,

m + 4/3 = (+/-) sqrt (-8/9),

m = - 4/3 (+/-) sqrt (-8/9), we HAVE two roots

NOTE: sqrt (-8/9) = sqrt ((-2)(4)/9) = sqrt ((-2)(2^2)/3^2) = sqrt ((-2)(2/3)^2) = 2/3 sqrt (-2)

m1 = -1.333 + 0.943 i

m2 = -1.333 - 0.943 i