Complete the square in (6x² - 13x + 6) and find its minimum value and the x-value where the minimum value occurs.
6x² - 13x + 6 = {(12x - 13)² - 25} / 24
6x² - 13x + 6 >= -25 / 24
{(12x - 13)² - 25} / 24 >= -25 / 24
minimum value = -25 / 24
(12x - 13)² = 0
x = 13 / 12
Complete the square in (10x² - 29x + 10) and find its minimum value and the x-value where the minimum value occurs.
10x² - 29x + 10 = {(20x - 29)² - 441} / 40
10x² - 29x + 10 >= -441 / 40
{(20x - 29)² - 441} / 40 >= -441 / 40
minimum value = -441 / 40
(20x - 29)² = 0
x = 29 / 20
Complete the square in (15x² - 34x + 15) and find its minimum value and the x-value where the minimum value occurs.
15x² - 34x + 15 = {(15x - 17)² - 64} / 15
15x² - 34x + 15 >= -64 / 15
{(15x - 17)² - 64} / 15 >= -64 / 15
minimum value = -64 / 15
(15x - 17)² = 0
x = 17 / 15