Complete the square in (10x² - 19x + 6) and find its minimum value and the x-value where the minimum value occurs.

10x² - 19x + 6 = {(20x - 19)² - 121} / 40

10x² - 19x + 6 >= -121 / 40

{(20x - 19)² - 121} / 40 >= -121 / 40

minimum value = -121 / 40

(20x - 19)² = 0

x = 19 / 20

Complete the square in (10x² - 21x + 9) and find its minimum value and the x-value where the minimum value occurs.

10x² - 21x + 9 = {(20x - 21)² - 81} / 40

10x² - 21x + 9 >= -81 / 40

{(20x - 21)² - 81} / 40 >= -81 / 40

minimum value = -81 / 40

(20x - 21)² = 0

x = 21 / 20

Complete the square in (15x² - 31x + 10) and find its minimum value and the x-value where the minimum value occurs.

15x² - 31x + 10 = {(30x - 31)² - 361} / 60

15x² - 31x + 10 >= -361 / 60

{(30x - 31)² - 361} / 60 >= -361 / 60

minimum value = -361 / 60

(30x - 31)² = 0

x = 31 / 30