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?

Answer 1

9x² - 42x + 49 is a perfect square in that (3x-7)² is the factored version.

if the square has an area of 64square meters the value of x would be 5.

(3x - 7)² = 64        (get the square root of each side)
√(3x - 7)² = √64
3x - 7 = 8                  (add 7 to both sides)
3x = 15                      (divide both sides by 3)
x = 5