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Simplifying 6x3 + 11x2 + 10x = 0 Reorder the terms: 10x + 11x2 + 6x3 = 0 Solving 10x + 11x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(10 + 11x + 6x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(10 + 11x + 6x2)' equal to zero and attempt to solve: Simplifying 10 + 11x + 6x2 = 0 Solving 10 + 11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.666666667 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 1.833333333x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 1.833333333x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 1.833333333x + x2 = 0 + -1.666666667 1.833333333x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 1.833333333x + x2 = -1.666666667 The x term is 1.833333333x. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333x + 0.8402777775 + x2 = -1.666666667 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = -1.666666667 + 0.8402777775 Combine like terms: -1.666666667 + 0.8402777775 = -0.8263888895 0.8402777775 + 1.833333333x + x2 = -0.8263888895 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = -0.8263888895 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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