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Simplifying 12x5 + 15x3 + -9x = 0 Reorder the terms: -9x + 15x3 + 12x5 = 0 Solving -9x + 15x3 + 12x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-3 + 5x2 + 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 '(-3 + 5x2 + 4x4)' equal to zero and attempt to solve: Simplifying -3 + 5x2 + 4x4 = 0 Solving -3 + 5x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 1.25x2 + x4 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.25x2 + 0.75 + x4 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.25x2 + x4 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.25x2 + x4 = 0 + 0.75 1.25x2 + x4 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.25x2 + x4 = 0.75 The x term is 1.25x2. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x2 + 0.390625 + x4 = 0.75 + 0.390625 Reorder the terms: 0.390625 + 1.25x2 + x4 = 0.75 + 0.390625 Combine like terms: 0.75 + 0.390625 = 1.140625 0.390625 + 1.25x2 + x4 = 1.140625 Factor a perfect square on the left side: (x2 + 0.625)(x2 + 0.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x2 + 0.625) equal to 1.068000468 and -1.068000468.Subproblem 1
x2 + 0.625 = 1.068000468 Simplifying x2 + 0.625 = 1.068000468 Reorder the terms: 0.625 + x2 = 1.068000468 Solving 0.625 + x2 = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x2 = 1.068000468 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x2 = 1.068000468 + -0.625 x2 = 1.068000468 + -0.625 Combine like terms: 1.068000468 + -0.625 = 0.443000468 x2 = 0.443000468 Simplifying x2 = 0.443000468 Take the square root of each side: x = {-0.665582803, 0.665582803}Subproblem 2
x2 + 0.625 = -1.068000468 Simplifying x2 + 0.625 = -1.068000468 Reorder the terms: 0.625 + x2 = -1.068000468 Solving 0.625 + x2 = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x2 = -1.068000468 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x2 = -1.068000468 + -0.625 x2 = -1.068000468 + -0.625 Combine like terms: -1.068000468 + -0.625 = -1.693000468 x2 = -1.693000468 Simplifying x2 = -1.693000468 Reorder the terms: 1.693000468 + x2 = -1.693000468 + 1.693000468 Combine like terms: -1.693000468 + 1.693000468 = 0.000000000 1.693000468 + 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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