My greatest mistake this week was working with completing the square when doing a quadratic equation. I fist though that when solving the square I was supposed to take (½b) ² then make C equal that number.
For example:
in the equation: x² – 4x – 7 = 0
I started off by taking half of –4 which is –2, then squaring it to get 4. From there I thought I had to make –7 equal 4. So, I added 11 making my equation:
(x –2) ² + 11 = 0
This gave me the wrong equation which led to errors when solving for x.
I do the same thing I started with but instead of making it equal 4, I took the 4 and made it equal –7.
To make 4 equal negative 7 I need to subtract 11, which makes the proper equation:
(x –2) ² – 11 = 0
From here I just square root everything getting
x – 2 = ±√11
Then I bring 2 to the other side which gets the final answer of:
x = ±√11 + 2
I learned that when I’m completing the square, I am not turning the value of C into b, but turning the value of (½b) ² into the value of C.
Next time, I’ll remember that completing the square is creating zero pairs. When I add a number to one side to complete the square, I move the constant first or subtract the same amount, this way the equation stays balanced.