Question

How to determine the value of k of the trinomial that is a perfect square?
9x^2 + kx + 49

Answer 1

Recall that \((3x + 7)^2 = 9x^2 + \cdots+49\).

Answer 2

If \(ax^2+bx+c\) is a perfect square then
\(b=2*\sqrt a*\sqrt c\)
here a=9 and c=49
Does that help @peekaboopork

Answer 3

(a + b)^2 = a^2 + 2ab + b^2
9x^2 = (3x)^2
49 = 7^2

(3x + 7)^2 = 9x^2 +42x + 49
(3x - 7)^2 = 9x^2 - 42x + 49

k = 42 or k = -42

Answer 4

A good way to find the middle term is to realize that in a perfect square, \(2ab\) is the middle term where \((a +b)^2 = a^2 + 2ab + b^2\). Here, \(b^2= 49 \iff b = 7\) and \(a^2 = 9x^2 \iff a = 3x \).

Answer 5

So what would \(2\cdot 7\cdot 3x\) be?

Answer 6

Actually I should have put \(\pm\), but it still would have the same result!