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9 June, 09:08

What factors add to get - 18 and multiply to get 75?

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  1. 9 June, 10:05
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    There are no whole-number solutions. Assuming you are trying to factorise the quadratic expression x^2 - 18x + 75, the discriminant (b^2 - 4ac) is 324 - 300 = 24. Although it is positive, so there are two solutions, 24 is not a square number so it does not factorise cleanly.

    To find the roots of the equation, I would complete the square:

    (x - 9) ^2 - 81 + 75 = 0

    (x - 9) ^2 - 6 = 0

    (x - 9) ^2 = 6

    x - 9 = ± √6

    x = 9 ±√6

    x = (9 + √6) or (9 - √6)
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