Today we are going to solve a Quadratic Equation
Here's the Equation:
X^2+5x=14 Looks complicated right! Well, Lets take it step by step....
- First we add or subtract terms which will enable us to set the equation to zero. Inorder for that to happen we need everything on the same side...for instances
x^2+5x=14
-14 -14 / x^2+5x-14=0 since you subtract 14 from one side you have to do it to the other side.
14 minus negative fourteen sets the right side of the equation to zero..... So we should end up with x^2+5x-14=0
2. We need to factor our remaining problem .We do this with the foil method. First, we look at the sign in front of the 14, it's negative, so when we foil, the signs in the ( )'s will be negative and positive. This way when we mulitiply the ( )"s together we will get a negative 14. This is what it will look like
(x- ) (x+ )
3. Next we will want to factor two numbers which when multiplied together will equal 14 and if subtracted will give me 5. So, let's make a list 1&14 or 2 &7. Let's try 2 &7
(x-2) (x+7) we'll foil to see if we get our original equation...
xtimes x = X^2, x times 7 is 7x x time -2 is -2x and -2 times 7 is -14 combined like terms.. which are 7x-2x which gives you 5x so we should end up with
x^2 + 5x-14 which is our original equation. We are not done yet :0( We still have to find the answer for x which we will do this way....
x-2=0 add 2 to each side which will equal to x=2
next since we have two answers (which you know that from your exponent of your first term) we have to do the same with our 7except we subtract since we have a positive 7 which will give us x=-7
So our complete answer is x=2 x=-7
Wella :0) Keep having fun
