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Simplifying 9x3 = 6x2 + 2x Reorder the terms: 9x3 = 2x + 6x2 Solving 9x3 = 2x + 6x2 Solving for variable 'x'. Reorder the terms: -2x + -6x2 + 9x3 = 2x + 6x2 + -2x + -6x2 Reorder the terms: -2x + -6x2 + 9x3 = 2x + -2x + 6x2 + -6x2 Combine like terms: 2x + -2x = 0 -2x + -6x2 + 9x3 = 0 + 6x2 + -6x2 -2x + -6x2 + 9x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -2x + -6x2 + 9x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + -6x + 9x2) = 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 '(-2 + -6x + 9x2)' equal to zero and attempt to solve: Simplifying -2 + -6x + 9x2 = 0 Solving -2 + -6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.6666666667x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.6666666667x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.6666666667x + x2 = 0 + 0.2222222222 -0.6666666667x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.6666666667x + x2 = 0.2222222222 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 0.2222222222 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.2222222222 + 0.1111111112 Combine like terms: 0.2222222222 + 0.1111111112 = 0.3333333334 0.1111111112 + -0.6666666667x + x2 = 0.3333333334 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.3333333334 Calculate the square root of the right side: 0.577350269 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.577350269 and -0.577350269.Subproblem 1
x + -0.3333333334 = 0.577350269 Simplifying x + -0.3333333334 = 0.577350269 Reorder the terms: -0.3333333334 + x = 0.577350269 Solving -0.3333333334 + x = 0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.577350269 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.577350269 + 0.3333333334 x = 0.577350269 + 0.3333333334 Combine like terms: 0.577350269 + 0.3333333334 = 0.9106836024 x = 0.9106836024 Simplifying x = 0.9106836024Subproblem 2
x + -0.3333333334 = -0.577350269 Simplifying x + -0.3333333334 = -0.577350269 Reorder the terms: -0.3333333334 + x = -0.577350269 Solving -0.3333333334 + x = -0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.577350269 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.577350269 + 0.3333333334 x = -0.577350269 + 0.3333333334 Combine like terms: -0.577350269 + 0.3333333334 = -0.2440169356 x = -0.2440169356 Simplifying x = -0.2440169356Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9106836024, -0.2440169356}Solution
x = {0, 0.9106836024, -0.2440169356}
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