Determine if 9x2 - 42x + 49 can b the area of a sq. what would the value of x have to be if the area of the sq is 64 sq mt. A = s2?

　
9x² − 42x + 49 = 64
(3x − 7)² = 64
3x − 7 = ± 8
3x = 7 ± 8
x = (7 ± 8) / 3
x = 5 or −1/3

Now side length of square must be positive.
[Since area = 64 sq m, then side length = 8m]

Are both values above valid for x?
Certainly, since x does NOT represent the side length of the square.
So x can be negative, it depends on how you define side length of square.

If side length = 3x−7, then x = 5 gives side = 3(5)−7 = 15 − 7 = 8
If side length = 7−3x, then x = −1/3 gives side = 7−3(−1/3) = 7+1 = 8

Any expression can be the area of a square if there are values of x for which the expression is positive. You mean, can 9x^2 - 42x + 49 be factorised into 2 identical linear factors?

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

We require (3x - 7)^2 = 64
3x - 7 = 8 or - 8
3x = 15 or - 1
x = 5 or - 1/3
A square side length cannot be negative.
x = 5 m