Complete the square in (4x² - 16x + 15) and find its minimum value and the x-value where the minimum value occurs.

4x² - 16x + 15 = (2x - 4)² - 1

4x² - 16x + 15 >= -1

(2x - 4)² - 1 >= -1

minimum value = -1

(2x - 4)² = 0

x = 2

Complete the square in (6x² - 19x + 15) and find its minimum value and the x-value where the minimum value occurs.

6x² - 19x + 15 = {(12x - 19)² - 1} / 24

6x² - 19x + 15 >= -1 / 24

{(12x - 19)² - 1} / 24 >= -1 / 24

minimum value = -1 / 24

(12x - 19)² = 0

x = 19 / 12

Complete the square in (6x² - 25x + 25) and find its minimum value and the x-value where the minimum value occurs.

6x² - 25x + 25 = {(12x - 25)² - 25} / 24

6x² - 25x + 25 >= -25 / 24

{(12x - 25)² - 25} / 24 >= -25 / 24

minimum value = -25 / 24

(12x - 25)² = 0

x = 25 / 12