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Simplifying 2x2 + -3x3 + 12x2 + -6x = 0 Reorder the terms: -6x + 2x2 + 12x2 + -3x3 = 0 Combine like terms: 2x2 + 12x2 = 14x2 -6x + 14x2 + -3x3 = 0 Solving -6x + 14x2 + -3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 14x + -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 '(-6 + 14x + -3x2)' equal to zero and attempt to solve: Simplifying -6 + 14x + -3x2 = 0 Solving -6 + 14x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4.666666667x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4.666666667x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4.666666667x + x2 = 0 + -2 -4.666666667x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4.666666667x + x2 = -2 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = -2 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = -2 + 5.444444448 Combine like terms: -2 + 5.444444448 = 3.444444448 5.444444448 + -4.666666667x + x2 = 3.444444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 3.444444448 Calculate the square root of the right side: 1.855921455 Break this problem into two subproblems by setting (x + -2.333333334) equal to 1.855921455 and -1.855921455.Subproblem 1
x + -2.333333334 = 1.855921455 Simplifying x + -2.333333334 = 1.855921455 Reorder the terms: -2.333333334 + x = 1.855921455 Solving -2.333333334 + x = 1.855921455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 1.855921455 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 1.855921455 + 2.333333334 x = 1.855921455 + 2.333333334 Combine like terms: 1.855921455 + 2.333333334 = 4.189254789 x = 4.189254789 Simplifying x = 4.189254789Subproblem 2
x + -2.333333334 = -1.855921455 Simplifying x + -2.333333334 = -1.855921455 Reorder the terms: -2.333333334 + x = -1.855921455 Solving -2.333333334 + x = -1.855921455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -1.855921455 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -1.855921455 + 2.333333334 x = -1.855921455 + 2.333333334 Combine like terms: -1.855921455 + 2.333333334 = 0.477411879 x = 0.477411879 Simplifying x = 0.477411879Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.189254789, 0.477411879}Solution
x = {0, 4.189254789, 0.477411879}
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