Example :  Use the quadratic formula to solve following equation.

                           x²+ 2x = 7

Solution

Here the important part is to ensure that before we begin using the quadratic formula that we contain the equation in standard form first.

                                                       x² + 2 x = 7

Thus, the first thing that we have to do here is to put the equation in standard form.

                                       x² + 2 x - 7 = 0

At this point we can recognize the values for employ in the quadratic formula. For this equation we contain.

                            a=1            b = 2               c = -7

Notice the "-" along with c. It is significant to ensure that we carry any minus signs along with the constants.

At this instance there actually isn't anything more to do other than plug in the formula.

For this equation there are two solutions. There is also some simplification which we can do. However we have to be careful.  One of the larger mistakes at this instance is to "cancel" two 2's in the numerator & denominator.  Recall that to cancel anything from the numerator or denominator then it has to be multiplied by the whole numerator or denominator. As the 2 in the numerator isn't multiplied by the whole denominator it can't be canceled out.

In order to do any simplification here we will first need to reduce the square root. At that instance we can do some canceling.

That's a much nicer answer to deal along with and thus we will almost always do this sort of simplification while it can be done.