Question 473045

Quadratic Formula is the method for solving quadratic equations that always work.  Not only that, but if you can remember the formula it’s a fairly simple process as well.

The important part here is to {{{make}}}{{{ sure}}} that before we start using the quadratic formula that we have the equation in standard form first.

     {{{ax^2 +-x+-c=0}}}


At this point we {{{can}}}{{{ identify}}} the values {{{a}}}, {{{b}}} and {{{c}}} for use in the quadratic formula.  It is {{{important}}} to {{{make}}}{{{ sure}}}that we carry any {{{minus}}}{{{ signs}}} along with the constants.

There is also some simplification that we can do.  We need to be careful however.  One of the {{{larger}}}{{{ mistakes}}} in this  example {{{x=(2+-sqrt(2))/2}}}  is to “{{{cancel}}}” to 2’s in the numerator and denominator.  Remember that in order to cancel anything from the numerator or denominator then it must be multiplied by the {{{whole}}}{{{ numerator}}} or {{{denominator}}}.  Since the 2 in the numerator isn’t multiplied by the whole denominator it {{{can’t}}} be canceled.

-don’t forget to convert square roots of negative numbers into complex numbers.  Also, {{{when}}}{{{ b}}} is {{{negative}}} be very careful with the substitution.  This is particularly true for the squared portion under the radical.  Remember that when you square a negative number it will become {{{positive}}}.  One of the more common mistakes here is to get in a hurry and {{{forget}}} to {{{drop}}} the {{{minus}}}{{{ sign}}} after you square {{{b}}}, so be careful.