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.

Example: X^2+8X+12=32

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.

Ex: 20-16=4

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

Complete and Continue