This week, we learned many different types of ways to solve quadratic equations. You can solve quadratic equations with factoring, zero product law, using square roots and using the quadratic formula. While solving all the equations, I found that each equations had a more suitable approach to it. Some approaches may be harder and some approaches may be easier.

One of the more interesting ones to me was using square roots to solve quadratic equations

Ex : $x^2 + 10x + 12 = 0$

In this case we know that this is not going to factor, so we use square roots to solve the equation $ax^2 + bx + c$

Step 1 : add a zero pair to the equation, to find out which number to use take the b, divide it by 2 and square it (shown in the second picture). Positive always first and then the negative (shown in the first)

Step 2 : When we take the first 3 terms of our new equations, it will give us a perfect square trinomial and then you would just simply add or subtract the rest of the numbers.

Step 3 : Our goal is to get x alone so the first step to doing so in this equation is to move the -13 to the other side giving us $(x+5)^2 = 13$

Step 4 : Now since this method is using square roots to solve for x, we would square root both sides because when you do something to one side, you must do it to the other side (shown in first picture)

Step 5 : You should always remember that when you put a square root into the equation, you must show that it is +/-

Step 6 : The final step is to get x by itself so we know that we can move 5 over to the other side which will give us our final answer : $x = -5$ +/- $\sqrt{13}$

This week I learned a lot of new things and learned many different methods to solving equations. Although this may not be the easiest method, it did interest me how we added zero pairs into the equation and it helped us solve it. The most straight forward method was using the quadratic formula, and the one I’m more familiar with is using factoring and 0 product law.