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................b2+3b=6

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b2 + 3b = 6

to complete the square you take 1/2 of the coefficient where the variable is of the first power then you square it and add it to both sides of the equation, in this case it's: (3/2)2 = 9/4

b2 + 3b + (9/4) = 6 + (9/4)    <--- remember that 6 = 24/4

[b + (3/2)]2 = 33/4

[b + (3/2)]2 - 33/4 = 0

Now multiply it back out to check, I'll expand the squared binomial for clarity

[b + (3/2)][b + (3/2)] - 33/4 = 0

b2 + (3/2)b + (3/2)b + 9/4 - 33/4 = 0

b2 + 3b - 24/4 = 0

b2 + 3b = 6