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Simplifying 8x3 + -3x + 12(11x2 + -3x) = 0 Reorder the terms: 8x3 + -3x + 12(-3x + 11x2) = 0 8x3 + -3x + (-3x * 12 + 11x2 * 12) = 0 8x3 + -3x + (-36x + 132x2) = 0 Reorder the terms: -3x + -36x + 132x2 + 8x3 = 0 Combine like terms: -3x + -36x = -39x -39x + 132x2 + 8x3 = 0 Solving -39x + 132x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-39 + 132x + 8x2) = 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 '(-39 + 132x + 8x2)' equal to zero and attempt to solve: Simplifying -39 + 132x + 8x2 = 0 Solving -39 + 132x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.875 + 16.5x + x2 = 0 Move the constant term to the right: Add '4.875' to each side of the equation. -4.875 + 16.5x + 4.875 + x2 = 0 + 4.875 Reorder the terms: -4.875 + 4.875 + 16.5x + x2 = 0 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + 16.5x + x2 = 0 + 4.875 16.5x + x2 = 0 + 4.875 Combine like terms: 0 + 4.875 = 4.875 16.5x + x2 = 4.875 The x term is 16.5x. Take half its coefficient (8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. 16.5x + 68.0625 + x2 = 4.875 + 68.0625 Reorder the terms: 68.0625 + 16.5x + x2 = 4.875 + 68.0625 Combine like terms: 4.875 + 68.0625 = 72.9375 68.0625 + 16.5x + x2 = 72.9375 Factor a perfect square on the left side: (x + 8.25)(x + 8.25) = 72.9375 Calculate the square root of the right side: 8.540345426 Break this problem into two subproblems by setting (x + 8.25) equal to 8.540345426 and -8.540345426.Subproblem 1
x + 8.25 = 8.540345426 Simplifying x + 8.25 = 8.540345426 Reorder the terms: 8.25 + x = 8.540345426 Solving 8.25 + x = 8.540345426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = 8.540345426 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = 8.540345426 + -8.25 x = 8.540345426 + -8.25 Combine like terms: 8.540345426 + -8.25 = 0.290345426 x = 0.290345426 Simplifying x = 0.290345426Subproblem 2
x + 8.25 = -8.540345426 Simplifying x + 8.25 = -8.540345426 Reorder the terms: 8.25 + x = -8.540345426 Solving 8.25 + x = -8.540345426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = -8.540345426 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = -8.540345426 + -8.25 x = -8.540345426 + -8.25 Combine like terms: -8.540345426 + -8.25 = -16.790345426 x = -16.790345426 Simplifying x = -16.790345426Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.290345426, -16.790345426}Solution
x = {0, 0.290345426, -16.790345426}
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