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

6x² - 19x + 10 = {(12x - 19)² - 121} / 24

6x² - 19x + 10 >= -121 / 24

{(12x - 19)² - 121} / 24 >= -121 / 24

minimum value = -121 / 24

(12x - 19)² = 0

x = 19 / 12

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

9x² - 21x + 10 = {(6x - 7)² - 9} / 4

9x² - 21x + 10 >= -9 / 4

{(6x - 7)² - 9} / 4 >= -9 / 4

minimum value = -9 / 4

(6x - 7)² = 0

x = 7 / 6

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

10x² - 31x + 15 = {(20x - 31)² - 361} / 40

10x² - 31x + 15 >= -361 / 40

{(20x - 31)² - 361} / 40 >= -361 / 40

minimum value = -361 / 40

(20x - 31)² = 0

x = 31 / 20