Algebra part 2
(Image courtesy of a student collaborating with us; Jacob Reeves)
The third way to solve quadratic equations is to complete the square.
Step 1: Check to make sure that the first term only has an X^2 in it) Remember, measure twice, cut once!
Step 2: subtract number outside equal sign by the last number term (called a constant)
32-12=20 and 12-12=0 (or blank)
Step 3: take the number in the middle (the one with the one x) divide it by 2 and multiply it by itself. That is called the MAGIC number.
(I included the magician hat as a way to remember what the number is.)
Example: 8/2=4. Then 4*4=16
then put that number in the empty place where the last term used to be. While leaving the other numbers alone.
Step 4: subtract number outside the equal sign by the MAGIC number.
now you have this:
step 5: take square root of first term and last term and keep the middle sign.
So it is: 2x+4
Step 6: You also take the square root of the number outside the equal sign.
√4=+2 and -2
Step 7: solve the two equations!
2x+4=2. And 2x+4=-2
step 8: write your answer (then plug in original formula to check if it comes out as zero)
x=-1 and x=-3
(Sometimes you may get a square root of a negative number. Normally that cannot happen but check the following meme below)
That is why in another section we will learn about the exception called “Imaginary Numbers”.
Fun Fact: The first to invent completing the square were the Babylonians though others later on realized how to do it. And that is why we have the Quadratic Formula