This week in pre-calculus, we learned 3 methods on how to solve a quadratic equation (an equation with a degree of 2).

My preferred way is called completing the square.

The example equation we are going to use is .

So first off we need to make sure that this equation = 0, which it does already.

Next we need to write out the equation like so:

+ ____ – ____ .

Now, to find the 2 numbers (which have to be the same), we take the b number which in this case is 6, we divide it in 2 and then square it.

Now we insert this number into the blank spaces (9).

.

Next we use the first three terms and treat it like a trinomial and factor it, since it is pretty easy to do. In this case we would have to find a 2 numbers that multiply to 9 since it is the c term, but add up to 6 since it is the b term. In this situation, the number is +3.

Next we evaluate the last two numbers, -9 +5.

Next we need to solve for x, so it is now just easy solving. First we remove the -4 and move it to the other side and become +4.

Now, since we eventually need to isolate the variable, we need to square both sides.

 

Now, we isolate x by removing the negative 3 from the left side and making it positive three on the other.

Now we have our solution!