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December 21, 2014

December 21, 2014

Posted by **Anonymous** on Monday, December 5, 2011 at 6:04am.

- math 117 -
**Reiny**, Monday, December 5, 2011 at 9:02amSometimes the factors just jump out at you , such as in

x^2 + 7x + 12 = 0

Usually, if the coefficients are single digits, it only takes a few seconds to see if it factors.

If the coefficients are 2 digits or more, I do a quick calculation of the determinant b^2 - 4ac

If that value is a perfect square, then I know the quadratic factors, but having found the discriminant, I am over half way there to get the answers, so I keep going with the formula anyway.

If the coefficient of x^2 is 1 and the middle term is even, I will**always**use completing the square over the formula.

It gives you the simplified radical solution, whereas the formula answer usually has to be simplified

e.g.

x^2 + 8x - 3 = 0

completing the square:

x^2 + 8x + 16 = 3 + 16

(x+4)^2 = 19

x+4 = ± √19

x = -4 ± √19

formula way:

x = (-8 ± √(64 - 4(1)(-3)) )/2

= (-8 ± √76)/2

= (-8 ± 2√19)/2

= -4 ± √19

Completing the square appears easier in this case.

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