SOLUTION: How do do you solve X^2-6x+9=100?

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Question 650909: How do do you solve X^2-6x+9=100?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You realize that
x%5E2-6x%2B9=%28x-3%29%5E2 and re-write the equation as
x-3%29%5E2=100
Since 10%5E2=100 and %28-10%29%5E2=100 ,
that leads you to the two solutions.
Either x-3=10 --> x=10%2B3 --> highlight%28x=13%29
or x-3=-10 --> x=-10%2B3 --> highlight%28x=-7%29

Not all equations will be that close to the solution.
If they had given you
x%5E2-6x-91=0 or the equivalent equation x%5E2-6x=91
you would have to realize that x%5E2-6x is almost x%5E2-6x%2B9=%28x-3%29%5E2
Then, adding 9 to both sides of the equal sign in x%5E2-6x=91 ,
you would get to x%5E2-6x%2B9=100
The adding of a number to get a perfect square is what math teachers call "completing the square."