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Complete the square on each of the following.
x^{2} -16x
Solution
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.
x^{2} -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.
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