Find the term that should be added to the expression to create a perfect square trinomial
2007-01-07 11:05:17 · 6 answers · asked by alexandra h 1 in Science & Mathematics ➔ Mathematics
please someone help this is due tommorrow and noone else can help me.
2007-01-07 11:06:58 · update #1
Given, ax^2 + bx, to complete the square add (b/2)^2.
The term will be: (b/2)^2 = (21/2)^2
2007-01-07 11:12:30 · answer #1 · answered by S. B. 6 · 2⤊ 0⤋
General rule: Take half the middle coefficient and
square it. If you add it to your expression it will
make a perfect square trinomial.
Here (21/2)² = 121/4.
We have to add 121/4 to make a square.
Check: (x + 11/2)² = x² + 21x + 121/4.
2007-01-07 19:10:05 · answer #2 · answered by steiner1745 7 · 2⤊ 1⤋
ax² + bx
becomes
ax² + bx + (b/2)²
as in
x² + 21x + (21/2)²
Which if you factor it out becomes:
(x + (21/2))(x + (21/2))
or
(x + 10.5)(x + 10.5)
a = 1, since it's just x², not 4x² etc.
I could be wrong, it's been a while.
2007-01-07 19:18:08 · answer #3 · answered by David G 2 · 1⤊ 1⤋
x² + 21x + 110 =
2007-01-07 19:12:06 · answer #4 · answered by aeiou 7 · 0⤊ 2⤋
x^2 + 21x + Q = (x + Z)^2 (using ^2 to be to-the-second-power or squared)
(x+Z)(x+Z) = x^2 + Zx + Zx + Z*Z
So we know Z+Z is 21 or 2Z = 21 or Z = 10.5
Q = 10.5^2 which is 110.25
x^2 + 21x + 110.25 is your answer.
Good reference below...
2007-01-07 19:11:39 · answer #5 · answered by Mario G 2 · 1⤊ 2⤋
x^2+21x+?=(x+a)^2
a^2=?
a=21^2/4
2007-01-07 19:38:06 · answer #6 · answered by Krisss 2 · 0⤊ 0⤋