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# X4 plus 3x3 - x2 - 9x - 6 equals 0?

Updated: 10/27/2022

Wiki User

14y ago

x4+ 3x3 - x2 - 9x - 6 = 0 (rewrite the equation, let -9x = -3x - 6x)

x4+ 3x3 - x2 - 3x - 6x - 6 = 0 (group terms)

(x4 - x2) + (3x3 - 3x) - (6x + 6) = 0

x(x2 - 1) + 3x(x2 - 1) - 6(x + 1) = 0 (use the difference of the squares, a2 - b2 = (a - b)(a + b))

x(x - 1)(x + 1) + 3x(x - 1)(x + 1) - 6(x + 1) = 0 (the common factor is x + 1)

(x + 1)[x(x - 1) + 3x(x - 1) - 6] = 0

(x + 1)(x2 - x + 3x2 - 3x - 6) = 0 (work with like terms)

(x + 1)(4x2 - 4x - 6) = 0 (factor out 2)

2(x + 1)(2x2 - 2x - 3) = 0

x + 1 = 0 or 2x2 - 2x - 3 = 0

x = -1 or

x = [-2 +/- square root of ((-2)2 - 4(2)(-3))]/2(2)

x = [-2 +/- square root of (4 + 24)]/4

x = -1/2 +/- (square root of 28)/4

x = -1/2 +/- 1/2(square root of 7)

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