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8 November, 13:53

What are the roots of the equation X squared plus 6X - 9 equals zero?

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  1. 8 November, 15:09
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    x = - 3 + 2√3 and

    x = - 3 - 2√3)

    Step-by-step explanation:

    x² + 6x - 9 = 0 can be solved in a variety of ways. Here I'll "complete the square" to solve for x:

    x² + 6x - 9 = 0 can be re-written as x² + 6x + 9 - 9 - 9 = 0. To do this, we identify the coefficient of x (which is 6), halve it (obtaining 3), square the result (obtaining 9), and then add and then subtract this result (9) between 6x - 9.

    Simplifying x² + 6x + 9 - 9 - 9 = 0 results in:

    (x + 3) ² = 18

    Taking the square root of both sides, we get:

    x + 3 = ±√18) = ±3√2

    Solving this for the two roots, we get:

    x = - 3 + 2√3 and

    x = - 3 - 2√3)
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