Answer:
y=-1.20 or -3.56
Step-by-step explanation:
4y^2+19y+17=0
subtract 7 from both sides to have
4y^2+19y=-17
Divide through by 4
y^2+19/4 y=-17/4
Complete the square of LHS to obtain
(y+19/8)^2 -(19/8)^2=-17/4
simplifying further we have
(y+19/8)^2=-17/4+(19)^2 /(8)^2 =-17/4+361/64=-272+361/64=89/64
i.e. (y+19/8)^2=89/64
taking the square root of both sides, we obtain
y+19/8=sqrt(89/64)=+ or - 1.18
which implies y= -19/8+or-1.18=2.38+or-1.18
either y = -2.38+1.18=-1.2
or y= -2.38-1.18= -3.56
Therefore, y=-1.20 or -3.56
