Applications of Quadratic Equations

Question

Find two consecutive negative odd integers such that 5 times the first plus the square of the second equals -14.

Answer 1

5F + S^2 = -14

F= S-2

5(S-2) +S^2 = -14

5S -10 +S^2 =-14

S^2 +5S + 4 = 0

(S+1)(S+4) = 0

S=-1, -4

F =S -2 -1-2 = -3

First number is -3, Second is -1