Solve the equation 3y^2 - 9y + 1 =0 by using completing square

Question

Solve the equation 3y² - 9y + 1 =0 by using completing square

Answer 1

Amber, the first thing we have to do is fivide everything by the leading coefficient.

 

y² - 3y + 1/3 = 0

 

Next, we are moving the 1/3 to the other side by subtracting.

 

y² - 3y = -1/3

 

To complete the square, take half of the 2nd coefficient (we call it b) and square it. (-3/2)² = 9/4. We add 9/4 to BOTH sides.

 

y² - 3y + 9/4 = -1/3 + 9/4

y² - 3y + 9/4 = 23/12

 

Now, the left side factors into a binomial squared, with the 2nd term being that -3/2.

 

(y - 3/2)² = 23/12

 

Now, we take the square root of both sides.

 

y - 3/2 = √(23/12)

y = √(23/12) + 3/2

 

 

Kind of a weird answer, but that's what we get using your equation.