Be the Professor- Blog Post 4

Completing the Square:

Hello Class! Today we will learn how to "Complete the Square". The reason we do this is because it helps put the quadratic equation into a neat format that can help you solve.

Lets do an example:

x² + 6x + 10 = 0

1. First, move the number thats alone (10) to the other side of the equal sign. 

                                x² + 6x = – 10

2. Next, Take the coefficient on the x-term and divide it by two(keeping the sign). Then square it and add it to both sides of the equation. 
    
                                                   x² + 6x = – 10

                                                       +3-->  +9
                                              x² + 6x+9 = -10 + 9

3. Then, convert the left side to a squared form (x + 3)². On the right side simplify (-1). 

                                                      (x + 3)² = –1
     
^{4. Take the square root of both sides and don't forget the} "±" . 
                                            x+3 =  ± square root of -1 = ± i



5. Solve for x and simplify.

                                  x = –3 ± i

Overall, if you use "Completing the Square" this technique will help you solve for quadratic equations. Make sure to do each step because each one helps you get one step closer to the answer.