How to Solve Quadratic Equations by Factoring (NancyPi)

MIT grad shows how to solve any quadratic equation by factoring. To skip to the shortcut trick, go to time 6:11. Nancy formerly of MathBFF explains the steps.

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The shortcut trick ("The Magic X") helps you factor any tough quadratic that doesn't begin with x^2 but instead begins w/ 2x^2 or 3x^2, or 4x^2, etc, so you can then solve.

1) IF QUADRATIC STARTS WITH X^2: It's faster to use the normal method for factoring in this case: trial and error. Ex: x^2 + 4x - 12. Find 2 numbers that multiply to the last number, -12, AND that add to the second coefficient, positive 4. First make a list of all pairs of #s that multiply to -12. Then check which pair also adds to 4. Write factors & solve by setting each = 0. Solve for x.

2) IF QUADRATIC STARTS WITH 2X^2 OR 3X^2 OR 4X^2, ETC:
A) First check if leading coefficient (2 or 3 or 4, etc) is an overall constant you can factor out of every term. If it is, factor it out first, then use Method #1 above to factor the X^2 expression that's left. Set factors = 0 & solve.
B) If a constant can't be factored out evenly from every term, it'll be faster & easier to use shortcut "magic X" method instead of Method #1. See it explained at time 6:11 in video. Set factors = 0 & solve.

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