This week we were introduced to the quadratic formula that we can use for any quadratic equation to solve for x. This is the last resort. First, you want to see if you can factor, then if you cannot, you want to make it a perfect square. If there is a complicated equation and it is hard to do either of those options, or the solution will be irrational, you can use the quadratic formula.

It looks like this;

The way to use this formula properly is to take your equation, for example, 2x²+3x-6=0. Then insert the correct numbers into their places on the formula.

A= x²

B= x

C= #

In this example A=2, B=3, C=-6. After you put all the information into the formula it will look like this;

From here, use BEDMAS to go through the question, and to start with the radiant is the best. In this situation, the radicand is also called the discriminant.

Once you solve only the discriminant, you can see if it is irrational, rational, has two or no solutions. If the discriminant is negative, there is no solution. If the discriminant is a perfect square, it is rational, there will be two solutions, and it was possible to factor. Lastly, if the number is positive, but is not a perfect square, it is an irrational number.

Going back to the example, this is how you work through it;

From here, since there is nothing in common for you to simplify, you will have two options for solutions due to the positive/negative symbol in front of the radicand.

The two options are…