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Solve using factorization method:
x2+7x+10=0

  • math -

    well two times five is ten
    and two plus five is 7
    so we have it made
    (x+2)(x+5) = 0
    that works if x+5 = 0 so x = -5
    and it works if x+2 = 0 so x = -2

  • math -

    x² + 7 x + 10 = 0

    The first term is, x² its coefficient is 1
    The middle term is, +7 x its coefficient is 7

    The last term, the constantis +10

    Multiply the coefficient of the first term by the constant 1 • 10 = 10

    Find two factors of 10 whose sum equals the coefficient of the middle term, which is 7


    - 10 • ( - 1 ) = 10

    - 10 + ( - 1 ) = - 10 - 1 = - 11


    - 5 • ( - 2 ) = 10

    - 5 + ( - 2 ) = - 5 - 2 = - 7


    - 2 • ( - 5 ) = 10

    - 2 + ( - 5 ) = - 2 - 5 = - 7


    - 1 • ( - 10 ) = 10

    - 1 + ( - 10 ) = - 1 - 10 = - 11


    1 • 10 = 10

    1 + 10 = 11


    2 • 5 = 10

    2 + 5 = 7

    That's it 2 and 5

    Rewrite the polynomial splitting the middle term using the factors 2 and 5

    x² + 2 x + 5 x + 10 = 0

    ( x² + 2 x ) + ( 5 x + 10 ) = 0

    x • ( x + 2 ) + 5 • ( x + 2 ) = 0

    ( x + 2 ) • x + ( x + 2 ) • 5 = 0

    ( x + 2 ) • ( x + 5 ) = 0


    x + 2 = 0

    x = - 2


    x + 5 = 0

    x = - 5

    The solutions are:

    x = - 5 and x = - 2

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