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Can someone help me solve this equation, please?
9x^3 + 18x^2 - 4x - 8 = 0
By inspection, -2 looks like it would work.
f(-2) = 9(-2)³+18(-2)² - 4(-2) - 8
= 0
Therefore -2 is a solution. If x=-2 is a solution, then x+2 is a root. Dividing the equation by x+2 (using long division) gives:
9x² - 4
which can be factorised to give (3x+2)(3x-2)
Therefore 9x³+18x² - 4x - 8 = (x+2)(3x+2)(3x-2), so the solutions are -2, -2/3 and 2/3.
Last edited by Daniel123 (2008-01-13 04:50:00)
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9x^3 + 18x^2 - 4x - 8 = 0
Looking at the equation, it can be simplified as
9x^2(x+2)-4(x+2) = 0
(9x^2-4)(x+2) = 0
Further simplifying 9x^2-4,
(3x-2)(3x+2)(x+2) = 0.
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Thank you very much for your help, guys.
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