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19 November, 15:52

What are the roots of the equation x^2+6x-9=0

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  1. 19 November, 18:13
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    x = approx. 1.24 or - 7.24

    Step-by-step explanation:

    It's hard to factor directly so we should use the quadratic formula or complete the square. I'm going to go with completing the square.

    x²+6x-9=0

    x²+6x=9

    x²+6x is the same as x²+2·3·x, in order to make this into the algebraic identity (A+B) ²=A²+2AB+B², we must add B², or in this case 3² to both sides. (A is x, B is 3)

    x²+6x+9=18

    (x+3) ² = 18

    x+3 = ±√18

    x = ±4.24 - 3 (approximately 4.24)

    First solution for x = 4.24-3 = 1.24

    Second solution for x = - 4.24-3 = - 7.24
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