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Simplifying 36x3 + -12x2 + -2x = 0 Reorder the terms: -2x + -12x2 + 36x3 = 0 Solving -2x + -12x2 + 36x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1 + -6x + 18x2) = 0 Ignore the factor 2.Subproblem 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 '(-1 + -6x + 18x2)' equal to zero and attempt to solve: Simplifying -1 + -6x + 18x2 = 0 Solving -1 + -6x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.05555555556 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + -0.3333333333x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + -0.3333333333x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + -0.3333333333x + x2 = 0 + 0.05555555556 -0.3333333333x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 -0.3333333333x + x2 = 0.05555555556 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 0.05555555556 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.05555555556 + 0.02777777779 Combine like terms: 0.05555555556 + 0.02777777779 = 0.08333333335 0.02777777779 + -0.3333333333x + x2 = 0.08333333335 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.08333333335 Calculate the square root of the right side: 0.288675135 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.288675135 and -0.288675135.Subproblem 1
x + -0.1666666667 = 0.288675135 Simplifying x + -0.1666666667 = 0.288675135 Reorder the terms: -0.1666666667 + x = 0.288675135 Solving -0.1666666667 + x = 0.288675135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.288675135 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.288675135 + 0.1666666667 x = 0.288675135 + 0.1666666667 Combine like terms: 0.288675135 + 0.1666666667 = 0.4553418017 x = 0.4553418017 Simplifying x = 0.4553418017Subproblem 2
x + -0.1666666667 = -0.288675135 Simplifying x + -0.1666666667 = -0.288675135 Reorder the terms: -0.1666666667 + x = -0.288675135 Solving -0.1666666667 + x = -0.288675135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.288675135 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.288675135 + 0.1666666667 x = -0.288675135 + 0.1666666667 Combine like terms: -0.288675135 + 0.1666666667 = -0.1220084683 x = -0.1220084683 Simplifying x = -0.1220084683Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4553418017, -0.1220084683}Solution
x = {0, 0.4553418017, -0.1220084683}
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