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Simplifying 6x3 + -2x2 + -18x = 0 Reorder the terms: -18x + -2x2 + 6x3 = 0 Solving -18x + -2x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-9 + -1x + 3x2) = 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 '(-9 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + -1x + 3x2 = 0 Solving -9 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.3333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.3333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.3333333333x + x2 = 0 + 3 -0.3333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.3333333333x + x2 = 3 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 = 3 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 3 + 0.02777777779 Combine like terms: 3 + 0.02777777779 = 3.02777777779 0.02777777779 + -0.3333333333x + x2 = 3.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 3.02777777779 Calculate the square root of the right side: 1.740051085 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 1.740051085 and -1.740051085.Subproblem 1
x + -0.1666666667 = 1.740051085 Simplifying x + -0.1666666667 = 1.740051085 Reorder the terms: -0.1666666667 + x = 1.740051085 Solving -0.1666666667 + x = 1.740051085 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 = 1.740051085 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.740051085 + 0.1666666667 x = 1.740051085 + 0.1666666667 Combine like terms: 1.740051085 + 0.1666666667 = 1.9067177517 x = 1.9067177517 Simplifying x = 1.9067177517Subproblem 2
x + -0.1666666667 = -1.740051085 Simplifying x + -0.1666666667 = -1.740051085 Reorder the terms: -0.1666666667 + x = -1.740051085 Solving -0.1666666667 + x = -1.740051085 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 = -1.740051085 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.740051085 + 0.1666666667 x = -1.740051085 + 0.1666666667 Combine like terms: -1.740051085 + 0.1666666667 = -1.5733844183 x = -1.5733844183 Simplifying x = -1.5733844183Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9067177517, -1.5733844183}Solution
x = {0, 1.9067177517, -1.5733844183}
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