Complete each square, then write the squared form

x^2 - 16x + ____
x^2 + 7x + _____

To complete the square you add half of the middle co-efficient squared:

x^2 - 16x + _____ (middle co-efficient = 16, half = 8, squared = 64)
x^2 + 7x + _____ (middle co-efficient = 7, half = 7/2, squared = 49/4)


x^2 - 16x + 64 squared form: (X-8)^2
x^2 + 7x + 49/4 squared form: (x + 7/2)^2

x^2 - 16x + 64 - 64 = (x-8)^2 -64
x^2 + 7x +49/4 - 49/4 = (x+7/2)^2 - 49/4

To complete the square you must add (b/2)^2 and then you must subtract it as well or add it to the other side of the equation so I showed it subtracted here for completeness.

x^2 - 16x + ____
2nd term = 2 × √(first term)(3rd term)
– 16x = 2√x² (3rd term)
– 16x = 2x√(3rd term)
– 8 = √(3rd term)
(– 8)² = [√(3rd term)]²
64 = (3rd term)
x^2 - 16x + __64__
= (x – 8)²

x^2 + 7x + _____
2nd term = 2 × √(first term)(3rd term)
7x = 2√x² (3rd term)
7x = 2x√(3rd term)
7/2 = √(3rd term)
(7/2)² = [√(3rd term)]²
49/4 = (3rd term)
x^2 + 7x + __49/4__
= (x + 7/2)²
------

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

x^2 + 7x + 49/4 = (x + 7/2)^2