Quadratic Equations (Part 2)

Today I decided to try something different while reading. I took the book and a piece of paper and pencil and wrote down the numbers from the problems on the blank piece of paper.

The narrative that explains the math makes me think of educational computer games I used to play when I was younger. There would be characters and they would seem to just do math equations for fun.

When Recordis suggested using the FOIL method I was reminded of my 8th grade class. I remember solving problems using this method, however I forgot what the letters stood for. After writing the problem down, I looked up "FOIL."

First - multiply the first term in each set of parenthesis: 4x * x = 4x^2

Outside - multiply the two terms on the outside: 4x * 2 = 8x

Inside - multiply both of the inside terms: 6 * x = 6x

Last - multiply the last term in each set of parenthesis: 6 * 2 = 12

I used this to help me look at the problem (x + 5)(x - 6) = 0

I tried it myself and got x^2- x - 30= 0, just like the next step in the book.

However, the next paragraph said to go back to the original equation, even though I was frustrated and confused, I decided it would be best to just keep reading.

I understood the next few sections on how to solve for 0 and get the two answers -5 and 6.


Then we were brought back to the quadratic equation. This really confused me, I thought we had the answer and that was it, what's the point in going back to the beginning? I kept reading hoping to find out.


The narrative about the King and his court was really starting to confuse me. I just didn't understand the point of all this assuming and guessing they did to solve problems. I was reminded of my 8th grade teacher telling me that I would have to keep plugging in numbers to find the two answers. I remember hating this explanation because to me guessing does not seem like a mathematical way of solving problems.

I kept reading until I got to a point that was clear to me. "You will never be able to solve every quadratic equation this way! Your trial-and-error factoring method will soon become helpless when you meet the equations I shall give you." I made a personal connection here, because this is how I felt when I was reading the earlier passages.


After a lot of trial-and-error, the King and his court determine the answer and create an equation to solve future problems quicker: The Quadratic Formula.

My only problem with this is, why all the explanation in the beginning of the chapter? All that back-story to the formula just confused me. Is that ever going to come in handy? Why couldn't they say: this is the formula, plug in the numbers to solve.

The rest of the chapter is practice problems, I'm going to go try a few of them now that I'm equipped with the formula.