For number 81 and 84 it asks me to Complete the square to form a perfect-square trinomial. Could someone explain how I find the answers to these two questions?

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)(x + 1/2)
x^2 + x + 1/4

Answer: x^2 + x + 1/4

For x^2 + 6x + ?:
For (x + ?)(x + ?), 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).
Multiplying this out:
(x + 3)^2
(x + 3)(x + 3)
x^2 + 6x + 9

Answer: x^2 + 6x + 9

apologiabiology apologiabiology · Answer 2 · 2016-04-24T22:47:04-04:00

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

blank is 1/4
blank is 9