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Simplifying 12x5 + 9x3 + -15x = 0 Reorder the terms: -15x + 9x3 + 12x5 = 0 Solving -15x + 9x3 + 12x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-5 + 3x2 + 4x4) = 0 Ignore the factor 3.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 '(-5 + 3x2 + 4x4)' equal to zero and attempt to solve: Simplifying -5 + 3x2 + 4x4 = 0 Solving -5 + 3x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 0.75x2 + x4 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.75x2 + 1.25 + x4 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.75x2 + x4 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.75x2 + x4 = 0 + 1.25 0.75x2 + x4 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.75x2 + x4 = 1.25 The x term is 0.75x2. 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. 0.75x2 + 0.140625 + x4 = 1.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x2 + x4 = 1.25 + 0.140625 Combine like terms: 1.25 + 0.140625 = 1.390625 0.140625 + 0.75x2 + x4 = 1.390625 Factor a perfect square on the left side: (x2 + 0.375)(x2 + 0.375) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x2 + 0.375) equal to 1.179247642 and -1.179247642.Subproblem 1
x2 + 0.375 = 1.179247642 Simplifying x2 + 0.375 = 1.179247642 Reorder the terms: 0.375 + x2 = 1.179247642 Solving 0.375 + x2 = 1.179247642 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 + x2 = 1.179247642 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x2 = 1.179247642 + -0.375 x2 = 1.179247642 + -0.375 Combine like terms: 1.179247642 + -0.375 = 0.804247642 x2 = 0.804247642 Simplifying x2 = 0.804247642 Take the square root of each side: x = {-0.896798552, 0.896798552}Subproblem 2
x2 + 0.375 = -1.179247642 Simplifying x2 + 0.375 = -1.179247642 Reorder the terms: 0.375 + x2 = -1.179247642 Solving 0.375 + x2 = -1.179247642 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 + x2 = -1.179247642 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x2 = -1.179247642 + -0.375 x2 = -1.179247642 + -0.375 Combine like terms: -1.179247642 + -0.375 = -1.554247642 x2 = -1.554247642 Simplifying x2 = -1.554247642 Reorder the terms: 1.554247642 + x2 = -1.554247642 + 1.554247642 Combine like terms: -1.554247642 + 1.554247642 = 0.000000000 1.554247642 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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