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Simplifying 0 = 4x3 + 3x2 + -6x Reorder the terms: 0 = -6x + 3x2 + 4x3 Solving 0 = -6x + 3x2 + 4x3 Solving for variable 'x'. Remove the zero: 6x + -3x2 + -4x3 = -6x + 3x2 + 4x3 + 6x + -3x2 + -4x3 Reorder the terms: 6x + -3x2 + -4x3 = -6x + 6x + 3x2 + -3x2 + 4x3 + -4x3 Combine like terms: -6x + 6x = 0 6x + -3x2 + -4x3 = 0 + 3x2 + -3x2 + 4x3 + -4x3 6x + -3x2 + -4x3 = 3x2 + -3x2 + 4x3 + -4x3 Combine like terms: 3x2 + -3x2 = 0 6x + -3x2 + -4x3 = 0 + 4x3 + -4x3 6x + -3x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 6x + -3x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(6 + -3x + -4x2) = 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 '(6 + -3x + -4x2)' equal to zero and attempt to solve: Simplifying 6 + -3x + -4x2 = 0 Solving 6 + -3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.75x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.75x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.75x + x2 = 0 + 1.5 0.75x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 0.75x + x2 = 1.5 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 1.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 1.5 + 0.140625 Combine like terms: 1.5 + 0.140625 = 1.640625 0.140625 + 0.75x + x2 = 1.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 0.375) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 0.375 = 1.280868846 Simplifying x + 0.375 = 1.280868846 Reorder the terms: 0.375 + x = 1.280868846 Solving 0.375 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.280868846 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.280868846 + -0.375 x = 1.280868846 + -0.375 Combine like terms: 1.280868846 + -0.375 = 0.905868846 x = 0.905868846 Simplifying x = 0.905868846Subproblem 2
x + 0.375 = -1.280868846 Simplifying x + 0.375 = -1.280868846 Reorder the terms: 0.375 + x = -1.280868846 Solving 0.375 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.280868846 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.280868846 + -0.375 x = -1.280868846 + -0.375 Combine like terms: -1.280868846 + -0.375 = -1.655868846 x = -1.655868846 Simplifying x = -1.655868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.905868846, -1.655868846}Solution
x = {0, 0.905868846, -1.655868846}
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