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How do people teach factoring a quadratic equation?
What are the different methods used?
That gives us $(x+6)^2=x^2+12x+36,$ which is too big by 9. That's the square of the amount that a is the wrong thing to use. The square root of 9 is 3. That means we should use a+3 and a-3, which is 6+3 and 6-3, 9 and 3.
Diagrams to follow if someone asks.
This method can even lead to the standard formula. Writing that slightly differently than usual, the solutions are -a+e and -a-e, where a is half the coefficient of x and e is the square root of the error. If the error is negative you have no real solutions.
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