This week I learned about how to solve a quadratic equation by making it into a perfect square. This is used when If you have a quadratic equation that is not factorable. The first step is to move the constant to the other side (if it’s all on one side to begin with), then you divide the number that’s  multiplying x by 2, then you square that number to get a new constant. If you add the constant you also have to add it on the other side. Next, you factor that side with the new constant, and it will give you – (x +/- a)², a = the square root of the constant you added. Next it’s simple algebra to find what x is, and remember if you add a square root you have to clarify that it could be positive or negative, so there’d be 2 answers.

This week I learned about how to use the zero product law to solve quadratic equations. The first step is to make sure 0 is on one side and the rest is on the other side. Then you factor out the equation. Since there is an equal sign, that means you can solve the equation (find x). You need to find 2 values for x that all both equal to 0. For example if one of my factors was (x-2), one of the solutions would be x = +2 (because -2 +2 = 0).

This week i learned about how to add and subtract radicals. At first I thought that adding radicals together would look like this: 1√2 + 4√3 = (1 + 4) √(2 + 3) = 5√5. I thought that you had to add the radicands together under one root sign, but my table group explained to me that this is how it works: 1√2 + 4√2 = (1 + 4) √2 = 5√2. The radicals do not get added together if the radicand is the same, you have to add or subtract the coefficients first and then keep the same root because its being multiplied by the coefficients.