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3x2-4x-15 = 0 (3x+5)(x-3) = 0 x = -5/3 or x = 3
Differentiate the function with respect to x: d/dx (x3 - 2x2 - 5x + 6) = 3x2 - 4x - 5 Set this derivative = 0 and solve. 3x2 - 4x - 5 = 0 implies that x = -0.7863 or 2.1196 (to 4 dp)
10x=x 9x=0 x=0
3x2 - 19x - 14 = 0 3x2 - 21x + 2x - 14 = 0 3x(x - 7) + 2(x - 7) = 0 (x - 7)(3x + 2) = 0 x - 7 = 0 or 3x + 2 = 0 x = 7 or x = -2/3
3x2 + 2x + 2 = 0 Can not be factored. You can however solve it for x: 3x2 + 2x = -2 x2 + 2x/3 = -2/3 x2 + 2x/3 + 1/9 = -2/3 + 1/9 (x + 1/9)2 = -5/9 x + 1/9 = ±√(-5/9) x = -1/9 ± i√(5/9) x = -1/9 ± i√5 / 3 x = -1/9 ± 3i√5 / 9 x = (-1 ± 3i√5) / 9