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Simplifying 3x3 + -11x2 + -9x = 0 Reorder the terms: -9x + -11x2 + 3x3 = 0 Solving -9x + -11x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-9 + -11x + 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 '(-9 + -11x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + -11x + 3x2 = 0 Solving -9 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.666666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -3.666666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.666666667x + x2 = 0 + 3 -3.666666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3.666666667x + x2 = 3 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 3 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 3 + 3.361111114 Combine like terms: 3 + 3.361111114 = 6.361111114 3.361111114 + -3.666666667x + x2 = 6.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 6.361111114 Calculate the square root of the right side: 2.522124326 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.522124326 and -2.522124326.Subproblem 1
x + -1.833333334 = 2.522124326 Simplifying x + -1.833333334 = 2.522124326 Reorder the terms: -1.833333334 + x = 2.522124326 Solving -1.833333334 + x = 2.522124326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 2.522124326 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.522124326 + 1.833333334 x = 2.522124326 + 1.833333334 Combine like terms: 2.522124326 + 1.833333334 = 4.35545766 x = 4.35545766 Simplifying x = 4.35545766Subproblem 2
x + -1.833333334 = -2.522124326 Simplifying x + -1.833333334 = -2.522124326 Reorder the terms: -1.833333334 + x = -2.522124326 Solving -1.833333334 + x = -2.522124326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -2.522124326 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.522124326 + 1.833333334 x = -2.522124326 + 1.833333334 Combine like terms: -2.522124326 + 1.833333334 = -0.688790992 x = -0.688790992 Simplifying x = -0.688790992Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.35545766, -0.688790992}Solution
x = {0, 4.35545766, -0.688790992}
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