Often, the simplest way
to solve "ax2 + bx + c= 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve
each factor. But sometimes the quadratic is too messy, or it doesn't factor at
all, or you just don't feel like factoring. While factoring may not always be
successful, the Quadratic Formula can always find the solution.
The Quadratic Formula
uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical
coefficients" of the quadratic equation they've given you to solve. The
Quadratic Formula isderived from the process of completing the square, and
is formally stated as:
For ax2 + bx + c =
0, the value of x is given by:
For the Quadratic
Formula to work, you must have your equation arranged in the form
"(quadratic) = 0". Also, the "2a" in the denominator of the Formula is underneath everything above, not just the square root. And it's a "2a" under there, not just a plain "2". Make sure that you are careful not to drop the square
root or the "plus/minus" in the middle of your calculations, or I can
guarantee that you will forget to "put them back" on your test, and
you'll mess yourself up. Remember that "b2" means "the
square of ALL of b, including its sign", so don't leave b2 being negative, even if b is negative, because the square of a negative is a positive.
In other words, don't be
sloppy and don't try to take shortcuts, because it will only hurt you in the
long run. Trust me on this!