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Simplifying 3x3 + -2x2 + -18x = 0 Reorder the terms: -18x + -2x2 + 3x3 = 0 Solving -18x + -2x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-18 + -2x + 3x2) = 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 '(-18 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -18 + -2x + 3x2 = 0 Solving -18 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.6666666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -0.6666666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.6666666667x + x2 = 0 + 6 -0.6666666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.6666666667x + x2 = 6 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 6 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 6 + 0.1111111112 Combine like terms: 6 + 0.1111111112 = 6.1111111112 0.1111111112 + -0.6666666667x + x2 = 6.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 6.1111111112 Calculate the square root of the right side: 2.472066162 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 2.472066162 and -2.472066162.Subproblem 1
x + -0.3333333334 = 2.472066162 Simplifying x + -0.3333333334 = 2.472066162 Reorder the terms: -0.3333333334 + x = 2.472066162 Solving -0.3333333334 + x = 2.472066162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 2.472066162 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.472066162 + 0.3333333334 x = 2.472066162 + 0.3333333334 Combine like terms: 2.472066162 + 0.3333333334 = 2.8053994954 x = 2.8053994954 Simplifying x = 2.8053994954Subproblem 2
x + -0.3333333334 = -2.472066162 Simplifying x + -0.3333333334 = -2.472066162 Reorder the terms: -0.3333333334 + x = -2.472066162 Solving -0.3333333334 + x = -2.472066162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -2.472066162 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.472066162 + 0.3333333334 x = -2.472066162 + 0.3333333334 Combine like terms: -2.472066162 + 0.3333333334 = -2.1387328286 x = -2.1387328286 Simplifying x = -2.1387328286Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8053994954, -2.1387328286}Solution
x = {0, 2.8053994954, -2.1387328286}
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