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19 September, 16:28

Solve the equation for all real solution 4y^2+19y+17=0

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  1. 19 September, 16:31
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    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
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