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Simplifying 6x3 + 34x2 + 2x = 0 Reorder the terms: 2x + 34x2 + 6x3 = 0 Solving 2x + 34x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(1 + 17x + 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 '(1 + 17x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + 17x + 3x2 = 0 Solving 1 + 17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 5.666666667x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 5.666666667x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 5.666666667x + x2 = 0 + -0.3333333333 5.666666667x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 5.666666667x + x2 = -0.3333333333 The x term is 5.666666667x. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667x + 8.027777782 + x2 = -0.3333333333 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = -0.3333333333 + 8.027777782 Combine like terms: -0.3333333333 + 8.027777782 = 7.6944444487 8.027777782 + 5.666666667x + x2 = 7.6944444487 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 7.6944444487 Calculate the square root of the right side: 2.773886164 Break this problem into two subproblems by setting (x + 2.833333334) equal to 2.773886164 and -2.773886164.Subproblem 1
x + 2.833333334 = 2.773886164 Simplifying x + 2.833333334 = 2.773886164 Reorder the terms: 2.833333334 + x = 2.773886164 Solving 2.833333334 + x = 2.773886164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 2.773886164 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 2.773886164 + -2.833333334 x = 2.773886164 + -2.833333334 Combine like terms: 2.773886164 + -2.833333334 = -0.05944717 x = -0.05944717 Simplifying x = -0.05944717Subproblem 2
x + 2.833333334 = -2.773886164 Simplifying x + 2.833333334 = -2.773886164 Reorder the terms: 2.833333334 + x = -2.773886164 Solving 2.833333334 + x = -2.773886164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -2.773886164 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -2.773886164 + -2.833333334 x = -2.773886164 + -2.833333334 Combine like terms: -2.773886164 + -2.833333334 = -5.607219498 x = -5.607219498 Simplifying x = -5.607219498Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.05944717, -5.607219498}Solution
x = {0, -0.05944717, -5.607219498}
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