complete the square on each of the

Question

Complete the square on each of the following.

                      x²  -16x

Solution

                          x² -16x

Here's the number which we'll insert to the equation.

                       ( -16 /2  ) = (-8)²  = 64

Notice that we put the minus sign here although it will always drop out after we square things. The cause for this will be clear in a second.  Now let's complete the square.

                                             x² -16 x + 64 =( x - 8)²

Now, it is a quadratic hopefully that you can factor fairly rapidly.  Though notice that this will always factor as x plus the blue number we calculated above i.e. in the parenthesis (in our case i.e. -8).  This is the cause for leaving the minus sign.  It ensures that we don't commit any mistakes in the factoring procedure.