Intermedia Algebra

Solve by factoring:
2a^2 − 3a = −5

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  1. 2a^2 - 3a = 5.

    2a^2 - 3a - 5 = 0,
    Use the AC Method:
    A*C = 2*(-5) = 10,
    2a^2 + (2a - 5a) -5 = 0,
    Group the 4 terms into 2 factorable pairs:
    (2a^2 + 2a) + (-5a - 5) = 0,
    Factor each binomial:
    2a(a + 1) -5(a + 1) = 0,
    Factor out a+1:
    (a + 1)(2a - 5) = 0,

    a + 1 = 0,
    a = -1.

    2a - 5 = 0,
    2a = 5,
    a = 2.5.

    Solution set: a = -1, and a = 2.5.

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