Question

HELP PLEASE!!! The area of a square is (16x2 − 8x + 1) square units. Determine the length of each side of the square by factoring the area expression completely.

Answer 1

4x - 1

Explanation:

given area of square :

16x² − 8x + 1

(4x)² -8x + 1

factor the equation

and this is a perfect square trinomial

a² - 2ab + b² = (a-b) (a-b)

(4x)² - 8x + 1 = (4x-1) (4x-1)

we know that the area A = s² (s stands for side)

substitute, (4x-1)² = s²

4x - 1 = s

therefore, the side of a square s = 4x - 1

Answer 2

Length of each side = (4x-1)

Explanation:

You could use the Quadratic formula to solve this, but there is a bit of a logical/intuitive gap you have to jump over at the end to get the answer.

For a straightforward mathematical explanation of what the area is equal to, you need to complete the square. From there you acknowledge that a square's sides are equal to each other and then you'll have your lengths.

My work is in the attachment. Comment with any questions.