Solve 15x² - 16x + 4 = 0 for x.

First method

15x² - 16x + 4 = 0

(3x - 2)(5x - 2) = 0

x = 2 / 3; 2 / 5

 

Second method

15x² - 16x + 4 = 0

225x² - 240x + 60 = 0

225x² - 240x + 64 = 4

(15x - 8)² = 4

15x - 8 = ±2

15x = 8 ± 2

x = (8 ± 2) / 15

x = 2 / 3; 2 / 5

 

Third method

15x² - 16x + 4 = 0

a = 15, b = -16 and c = 4

b² - 4ac = 16

x = (16 ± √16) / 30

x = (16 ± 4) / 30

x = (8 ± 2) / 15

x = 2 / 3; 2 / 5

 

Solve 15x² - 19x + 6 = 0 for x.

First method

15x² - 19x + 6 = 0

(3x - 2)(5x - 3) = 0

x = 2 / 3; 3 / 5

 

Second method

15x² - 19x + 6 = 0

900x² - 1,140x + 360 = 0

900x² - 1,140x + 361 = 1

(30x - 19)² = 1

30x - 19 = ±1

30x = 19 ± 1

x = (19 ± 1) / 30

x = 2 / 3; 3 / 5

 

Third method

15x² - 19x + 6 = 0

a = 15, b = -19 and c = 6

b² - 4ac = 1

x = (19 ± √1) / 30

x = (19 ± 1) / 30

x = 2 / 3; 3 / 5

 

Solve 25x² - 25x + 6 = 0 for x.

First method

25x² - 25x + 6 = 0

(5x - 2)(5x - 3) = 0

x = 2 / 5; 3 / 5

 

Second method

25x² - 25x + 6 = 0

100x² - 100x + 24 = 0

100x² - 100x + 25 = 1

(10x - 5)² = 1

10x - 5 = ±1

10x = 5 ± 1

x = (5 ± 1) / 10

x = 3 / 5; 2 / 5

 

Third method

25x² - 25x + 6 = 0

a = 25, b = -25 and c = 6

b² - 4ac = 25

x = (25 ± √25) / 50

x = (25 ± 5) / 50

x = (5 ± 1) / 10

x = 3 / 5; 2 / 5