To complete the square, you want to add a number that will allow the number to be factored into terms of the form (x + ?)^2
For x^2 + x + ?: For (x + ?)(x + ?), we want both ? to add up the 1 (the number in front of x), and since both ? have to be the same number, ? must equal 1/2 (1/2 + 1/2 = 1). Multiplying this out: (x + 1/2)^2 (x + 1/2)<span>(x + 1/2) </span>x^2 + x + 1/4
Answer: x^2 + x + 1/4
For x^2 + 6x + ?: For (x + ?)(x + ?)<span>, we want both ? to add up the 6 (the number in front of x), and since both ? have to be the same number, ? must equal 3 (3 + 3 = 6). </span> Multiplying this out: (x + 3)^2 (x + 3)<span>(x + 3) </span>x^2 + 6x + 9
Completeing the square
in form
ax^2+b+c=0
1st move c to other side or ignore it if not present
2nd. make sure a=1, if not, divide both sides by a
3rd divide b by 2 and squaer that ((b/2)^2) and add that to both sides
factor perfect square
81.
ignore c
a=1 so good
b=1 so 1/2, then squaer that which is 1/4
that is the blank space
1/4
84.
ignore c since not present
a is equal to 1
b=6 so 1/2 of that is 3, 3^2=9
9 is the blank
81. blank is 1/4
84. blank is 9
