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Simplifying 4x3 + 12x2 + -18x = 0 Reorder the terms: -18x + 12x2 + 4x3 = 0 Solving -18x + 12x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-9 + 6x + 2x2) = 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 '(-9 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying -9 + 6x + 2x2 = 0 Solving -9 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 3x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 3x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 3x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 3x + x2 = 0 + 4.5 3x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 3x + x2 = 4.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 4.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 4.5 + 2.25 Combine like terms: 4.5 + 2.25 = 6.75 2.25 + 3x + x2 = 6.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + 1.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x + 1.5 = 2.598076211 Simplifying x + 1.5 = 2.598076211 Reorder the terms: 1.5 + x = 2.598076211 Solving 1.5 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.598076211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.598076211 + -1.5 x = 2.598076211 + -1.5 Combine like terms: 2.598076211 + -1.5 = 1.098076211 x = 1.098076211 Simplifying x = 1.098076211Subproblem 2
x + 1.5 = -2.598076211 Simplifying x + 1.5 = -2.598076211 Reorder the terms: 1.5 + x = -2.598076211 Solving 1.5 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.598076211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.598076211 + -1.5 x = -2.598076211 + -1.5 Combine like terms: -2.598076211 + -1.5 = -4.098076211 x = -4.098076211 Simplifying x = -4.098076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.098076211, -4.098076211}Solution
x = {0, 1.098076211, -4.098076211}
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