SOLUTION: solve the equation y^2-6y+9=0

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Question 621376: solve the equation y^2-6y+9=0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Sometimes the easiest way to solve a quadratic equation is by factoring, and this is a great example of that.
y%5E2-6y%2B9 should be recognized as the square of a binomial, because
y%5E2 is the square of y,
%2B9 is the square of 3 and of -3,
and -6y=2%2Ay%2A%28-3%29 is double the product of y and -3.
So, y%5E2-6y%2B9=%28y-3%29%5E2 and then
y%5E2-6y%2B9=0 ---> %28y-3%29%5E2=0 ---> y-3=0 ---> highlight%28y=3%29
Not all quadratic equations can be solved by factoring, but when it is possible, it is easier than dealing with the dreaded quadratic formula.