Question

3y^2+5y=12 complete the square

Answer 1

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