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Simplifying (2x3 + -2x2 + 4x) + (3x3 + 6x2 + -12x) = 0 Reorder the terms: (4x + -2x2 + 2x3) + (3x3 + 6x2 + -12x) = 0 Remove parenthesis around (4x + -2x2 + 2x3) 4x + -2x2 + 2x3 + (3x3 + 6x2 + -12x) = 0 Reorder the terms: 4x + -2x2 + 2x3 + (-12x + 6x2 + 3x3) = 0 Remove parenthesis around (-12x + 6x2 + 3x3) 4x + -2x2 + 2x3 + -12x + 6x2 + 3x3 = 0 Reorder the terms: 4x + -12x + -2x2 + 6x2 + 2x3 + 3x3 = 0 Combine like terms: 4x + -12x = -8x -8x + -2x2 + 6x2 + 2x3 + 3x3 = 0 Combine like terms: -2x2 + 6x2 = 4x2 -8x + 4x2 + 2x3 + 3x3 = 0 Combine like terms: 2x3 + 3x3 = 5x3 -8x + 4x2 + 5x3 = 0 Solving -8x + 4x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + 4x + 5x2) = 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 '(-8 + 4x + 5x2)' equal to zero and attempt to solve: Simplifying -8 + 4x + 5x2 = 0 Solving -8 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 0.8x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 0.8x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 0.8x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 0.8x + x2 = 0 + 1.6 0.8x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 0.8x + x2 = 1.6 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 1.6 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 1.6 + 0.16 Combine like terms: 1.6 + 0.16 = 1.76 0.16 + 0.8x + x2 = 1.76 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + 0.4) equal to 1.326649916 and -1.326649916.Subproblem 1
x + 0.4 = 1.326649916 Simplifying x + 0.4 = 1.326649916 Reorder the terms: 0.4 + x = 1.326649916 Solving 0.4 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.326649916 + -0.4 x = 1.326649916 + -0.4 Combine like terms: 1.326649916 + -0.4 = 0.926649916 x = 0.926649916 Simplifying x = 0.926649916Subproblem 2
x + 0.4 = -1.326649916 Simplifying x + 0.4 = -1.326649916 Reorder the terms: 0.4 + x = -1.326649916 Solving 0.4 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.326649916 + -0.4 x = -1.326649916 + -0.4 Combine like terms: -1.326649916 + -0.4 = -1.726649916 x = -1.726649916 Simplifying x = -1.726649916Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.926649916, -1.726649916}Solution
x = {0, 0.926649916, -1.726649916}
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