Решите уравнение:

31x+77=15 (x+1) ^2

31x+77=15 (x+1) ²

31x+77=15 (x²+2x+1)

31x+77=15x²+30x+15

15x²+30x+15-31x-77=0

15x²-x-62=0

D=1-4*15 * (-62) = 3721

x1,2=

x1=

x2=

31x + 77 = 15 (x^2 + 2x + 1)

31x + 77 = 15x^2 + 30x + 15

- 15x^2 + 31x - 30x + 77 - 15 = 0

- 15x^2 + x + 62 = 0

15x^2 - x - 62 = 0

D = b^2 - 4ac = 1 - 4*15 * (-62) = 1 + 3720 = 3721 = 61^2

x1 = (1 + 61) / 30 = 62 / 30 = 31 / 15 = 2 целых 1/15

x2 = (1 - 61) / 30 = - 60 / 30 = - 2