49-apex
3
9
82+8 = 72
9 needs to be added to complete the square. When squaring (x + n), the result is x2 + 2nx + n2. We have +10x, so n must be 10/2 = 5. Thus: (x + 5)2 = x2 +10x + 25 = x2 +10x + 14 + 9 So 9 needs to be added to complete the square, giving: x2 +10x + 14 = (x + 5)2 - 9
-7
3
9
102 +10=110
82+8 = 72
-3
144
9 needs to be added to complete the square. When squaring (x + n), the result is x2 + 2nx + n2. We have +10x, so n must be 10/2 = 5. Thus: (x + 5)2 = x2 +10x + 25 = x2 +10x + 14 + 9 So 9 needs to be added to complete the square, giving: x2 +10x + 14 = (x + 5)2 - 9
-7
49/4 or 12.25
Adding 100 completes the square. { I wonder why you want to complete the square when the expression already factors as x(x-20) }.
1 is the number you are looking for.1 + 12 = 1 + 1 = 2.QED
To complete the square for the expression (x^2 + 9x), take half of the coefficient of (x) (which is 9), square it, and add that value. Half of 9 is (4.5), and squaring it gives (20.25). Therefore, the number that must be added is (20.25). Thus, the completed square form is ((x + 4.5)^2).