b^{2}+3b=6

**b ^{2} + 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**

**b ^{2} + 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**

**b ^{2} + (3/2)b + (3/2)b + 9/4 - 33/4 = 0**

**b ^{2} + 3b - 24/4 = 0**

**b ^{2} + 3b = 6**