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Simplifying 3x3 + -17x2 + 3x = 0 Reorder the terms: 3x + -17x2 + 3x3 = 0 Solving 3x + -17x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + -17x + 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 '(3 + -17x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + -17x + 3x2 = 0 Solving 3 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5.666666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -5.666666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5.666666667x + x2 = 0 + -1 -5.666666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5.666666667x + x2 = -1 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 = -1 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = -1 + 8.027777782 Combine like terms: -1 + 8.027777782 = 7.027777782 8.027777782 + -5.666666667x + x2 = 7.027777782 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 7.027777782 Calculate the square root of the right side: 2.650995621 Break this problem into two subproblems by setting (x + -2.833333334) equal to 2.650995621 and -2.650995621.Subproblem 1
x + -2.833333334 = 2.650995621 Simplifying x + -2.833333334 = 2.650995621 Reorder the terms: -2.833333334 + x = 2.650995621 Solving -2.833333334 + x = 2.650995621 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 = 2.650995621 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 2.650995621 + 2.833333334 x = 2.650995621 + 2.833333334 Combine like terms: 2.650995621 + 2.833333334 = 5.484328955 x = 5.484328955 Simplifying x = 5.484328955Subproblem 2
x + -2.833333334 = -2.650995621 Simplifying x + -2.833333334 = -2.650995621 Reorder the terms: -2.833333334 + x = -2.650995621 Solving -2.833333334 + x = -2.650995621 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 = -2.650995621 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -2.650995621 + 2.833333334 x = -2.650995621 + 2.833333334 Combine like terms: -2.650995621 + 2.833333334 = 0.182337713 x = 0.182337713 Simplifying x = 0.182337713Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.484328955, 0.182337713}Solution
x = {0, 5.484328955, 0.182337713}
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