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Simplifying 6x3 + -22x2 + 9x = 0 Reorder the terms: 9x + -22x2 + 6x3 = 0 Solving 9x + -22x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(9 + -22x + 6x2) = 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 + -22x + 6x2)' equal to zero and attempt to solve: Simplifying 9 + -22x + 6x2 = 0 Solving 9 + -22x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -3.666666667x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -3.666666667x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -3.666666667x + x2 = 0 + -1.5 -3.666666667x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -3.666666667x + x2 = -1.5 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 = -1.5 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = -1.5 + 3.361111114 Combine like terms: -1.5 + 3.361111114 = 1.861111114 3.361111114 + -3.666666667x + x2 = 1.861111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 1.861111114 Calculate the square root of the right side: 1.364225463 Break this problem into two subproblems by setting (x + -1.833333334) equal to 1.364225463 and -1.364225463.Subproblem 1
x + -1.833333334 = 1.364225463 Simplifying x + -1.833333334 = 1.364225463 Reorder the terms: -1.833333334 + x = 1.364225463 Solving -1.833333334 + x = 1.364225463 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 = 1.364225463 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 1.364225463 + 1.833333334 x = 1.364225463 + 1.833333334 Combine like terms: 1.364225463 + 1.833333334 = 3.197558797 x = 3.197558797 Simplifying x = 3.197558797Subproblem 2
x + -1.833333334 = -1.364225463 Simplifying x + -1.833333334 = -1.364225463 Reorder the terms: -1.833333334 + x = -1.364225463 Solving -1.833333334 + x = -1.364225463 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 = -1.364225463 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -1.364225463 + 1.833333334 x = -1.364225463 + 1.833333334 Combine like terms: -1.364225463 + 1.833333334 = 0.469107871 x = 0.469107871 Simplifying x = 0.469107871Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.197558797, 0.469107871}Solution
x = {0, 3.197558797, 0.469107871}
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