Question

Determine if 9x2 - 42x + 49 can be the area of a square. If so, what would the value of x have to be if the area of the square is 64 square meters? A = s2 explain your reasoning.

Answer 1

$factorizing \: \: given \: \: polynomial \\ 9 {x}^{2} - 42x + 49 = {(3x - 7)}^{2} \: is \: perfect \: \: square \\ thus \: \: it \: \: can \: \: be \: \: the \: \: area \: of \: \: square \\ given \\ 9 {x}^{2} - 42x + 49 = 64 \\ {(3x - 7)}^{2} = { (+ \: \: or \: \: - 8)}^{2} \\ 3x - 7 = + \: \: or \: \: - 8 \\ x = 5 \: \: or \: \: \frac{ - 1}{3}$