SOLUTION: John used completing the square to find the zeros of the function y=9x^2-12x-33. Can someone please show please show me the steps for solving this ???

Question 123486: John used completing the square to find the zeros of the function y=9x^2-12x-33. Can someone please show please show me the steps for solving this ???
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
John used completing the square to find the zeros of the function
y = 9x^2 - 12x - 33
:
Find the zeros:
9y^2 - 12x - 33 = 0
:
When completing the square, y^2 has to have a coefficient of 1,
divide each term by 9:
y^2 - x - = 0
:
We are going to replace the 3rd term with a value that will make it a square
Add to both sides:
y^2 - x + ____ =
:
We can determine the 3rd term as follows:
Divide the coefficient of x by 2; that would be
Square this value; that would be reduced to
:
y^2 - x + = + ; we have to add the same amt to both sides to keep an equation
:
y^2 - x + = ;
Now it is a square, and can be factored to:
(y - ) (y - ) =
or
(y - )^2 =
:
Find the square root of both sides and we have;
y - = +/-
:
y = + +/- add 2/3 to both sides
We can factor 1/3 out of the radical, gets rid of the denominator inside the radical
y = +/-
or
y =
and
y =
:
There are a lot of steps here. I hope you will take the time to study each one
If you have any questions, you can email me. Ankor

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