Hello from MrBillDoesMath!
Answer:
(y+ 5/6)^2 = 169/36
Discussion:
3y^2+5y=12 => (divide both sides by 3)
y^2 + (5/3)y = 12/3 = 4 =>
Add\subtract the square of one-half the coefficient of y:
( y^2 + (5/3)y + (5/6)^2) - (5/6)^2 =4 (add (5/6)^2 to both sides)
(y^2 + (5/3)y + (5/6)^2 = 4 + (5/6)^2 =>
(y+ 5/6)^2 = 4 + (5/6)^2 = 4 + (25/36) =
(144+25)/36 = 169/36
So
(y+ 5/6)^2 = 169/36
We can also solve for y by taking the square root of both sides:
(y + 5/6) = sqrt(169/36)
= +\- 13/6 ( as 169 = 13*13 and 36 = 6*6)
y = (-5/6) +\- 13/6
Thank you,
MrB