As with factoring, the quadratic formula won't really do what we want it to do and until we clear out one side.
So remember, before using the quadratic formula the equation must equal 0 and it must be in order.
Your goal before you use the quadratic formula is to get an equation that looks like this, AX squared plus BX plus
C equals 0 because if you remember the quadratic formula comes directly from that A, B, and C.
The quadratic formula is negative B plus or minus the square root of B squared minus 4AC all over 2A.
Again make sure to memorize that formula, you will need to memorize it for the test.
So let's take a look at example one.
Example one, does not quiet have a side cleared out so we need to start by doing that.
We'll add 7x to both sides and we'll also subtract 15 from both sides and if I do that, I'm going to get 2x
squared plus 7x minus 15 equals 0.
Now I can use the quadratic formula, X is going to equal the negative of B, well B is 7, plus or minus the square
root of B squared, B is still 7, minus 4 times 2 times negative 15 all over 2 times A which is 2 and then from
here on out as with the last section, this is really just a matter of simplifying.
We're just going to clean everything up until it looks as nice as it can.
Well the negative of 7 is obviously negative 7 we're going to do plus or minus, 7 squared is obviously 49.
Negative 4 times 2 times negative 15 all works out to positive 120, we're going to divide by 4.
Again make sure your fraction bar covers the entirety of the top, it is a different answer if you don't do that.
We'll have negative 7 plus or minus the square root of 169 over 4, well fortuitously 169 has a nice square root, it
is 13 exactly.
After this step we will have negative 7 plus or minus the square root of 13 all over 4 and again to cap this off when you have
integers like this when your answers are nice like this, you do need to actually calculate both answers.
Well negative 7 minus 13 over 4 is negative 20 over 4 which is 5.
Negative 7 plus 13 over 4 is 6/4 which reduces to 3/2, negative 5 is your first answer so you have negative 5
and 3/2.
So for example two, again we need to clear out both sides.
We'll subtract 7 from both sides, we get 3x squared plus 5x plus 2 minus 5 equals 0.
Again we'll put all of this into the quadratic formula, we have the negative of 5 plus or minus the square root of 5
squared minus 4 times 3 times negative 5 and again you divide that by 2 times A, A in this case is 3.
And again we simplify, negative of 5 is negative 5 plus or minus the square root of 25 then negative 4
times negative 5 times 3 works out to 60 and we divide that by 6.
25 plus 60 is obviously 85, unfortunately 85 does not have a nice square root.
So, we're kind of up the creek there.
This is as simple as this problem gets but the good news is you don't have to do any simplifying.
So just remember that before you can use the quadratic formula you need to get 0 on one side.
