Penjelasan dengan langkah-langkah:

1) x² + x = 72

x² + x - 72 = 0

a = 1

b = 1

c = -72

x = -b ± √b² - 4ac/2a

x = -1 ± √(-1)² - 4(1)(-72)/2(1)

x = -1 ± √1 + 288/2

x = -1 ± √289/2

x = -1 ± 17/2

x = -1 + 17/2

x = 16/2 = 8

x = -1 - 17/2

x = -18/2 = -9

Maka, HP = { -9, 8 }

2) 2x² + 7x + 5 = 0

a = 2

b = 7

c = 5

x = -b ± √b² - 4ac/2a

x = -7 ± √7² - 4(2)(5)/2(2)

x = -7 ± √49 - 40/4

x = -7 ± √9/4

x = -7 ± 3/4

x = -7 + 3/4

x = -4/4 = -1

x = -7 - 3/4

x = -10/4 = -2,5 atau -5/2

HP = {-5/2, -1}

3) 6x² - 11x + 3 = 0

a = 6

b = -11

c = 3

x = -b ± √b² - 4ac/2a

x = -(-11) ± √(-11)² - 4(6)(3)/2(6)

x = 11 ± √121 - 72/12

x = 11 ± √49/12

x = 11 ± 7/12

x = 11 + 7/12

x = 18/12 = 1,5 = ³/2

x = 11-7/12

x = 4/12 = ⅓ atau 0,33....

HP = {⅓, ³/2}

4) 2x² - 7x = 0

a = 2

b = -7

c = 0

x = -b ± √b² - 4ac/2a

x = -(-7) ± √(-7)² - 4(2)(0)/2(2)

x = 7 ± √49 - 0/4

x = 7 ± 7/4

x = 7 + 7/4

x = 14/4 = 3,5 = ⁷/2

x = 7 - 7/4

x = 0/4 = 0

HP = {0, ⁷/2}