Answer:
8 more unit of tiles
Explanation:
The function is given as;
f(x) = x² - 6x + 1
Now, we want to add more unit tiles to complete the square.
The given function(f(x)) is of the order 2 due to the highest power of 2 attached to x, but the side of the square will be of the order 1.
Now, Let's make a general order 1 expression ax + b to be the side of the square.
From the function forming the square after adding some p unit tiles, we have;
f(x) + p = (side of square)²
Thus;
x² - 6x + 1 + p = (ax + b)²
x² - 6x + 1 + p = a²x² + 2abx + b²
Comparing both sides of the equation, we have;
a² = 1
2ab = 6
b² = 1 + p
From a² = 1, a = 1
From 2ab = 6,putting 1 for a, we have;
2(1)b = 6
b = 6/2
b = 3
From b² = 1 + p
Putting 3 for b, we have;
3² = 1 + p
9 = 1 + p
9 - 1 = p
p = 8
Thus, 8 more unit of tiles are required to complete the square.