Solving trinomial squares?

Question

Hey I need help on this problem:

81x^2 - 126x + 49 = 16

btw, I'm confused about how you fill in the first parentheses. My friend said to start the problem you first put (9x-7)^2 = 16 but where does the 7 and 9 come from? thanks.
20 minutes ago - 3 days left to answer.

Answer 1

7² = 49, 9² = 81, and 126 = 2(7•9)
(9x - 7)² = 16
9x - 7 = 4
9x = 11
x = 11/9 or
9x - 7 = -4
9x = 3
x = 1/3

Answer 2

You have to spot that 81 and 49 are square numbers, meaning they are the squares of 9 and 7. That's where they come from.

Then you have to spot that 9 x 7 = 63, and that 63+63 = 126

With these 'lucky' numbers (meaning that the question was rigged so that it would work out nicely) we can write down the square equation:

(9x - 7)(9x - 7) = 16

we chose the subtraction, the negative sign, to give the -126 element, see what happens next:

expanding this bit by bit gives

9x(9x - 7) - 7(9x - 7) = 16
81x^2 - 63x -63x +49 =16
81x^2 -126x +49 = 16 hey presto, our starting point

Solving is then easy:

(9x-7)^2 = 16
take the square root on both sides

9x - 7 = +- 4

then there are two answers corresponding to the + and -

9x - 7 = +4
9x = 11
and x = 11/9

and
9x - 7 = -4
9x = 3
x = 3/9 = 1/3