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Simplifying 3x5 + 8x3 + 2x = 0 Reorder the terms: 2x + 8x3 + 3x5 = 0 Solving 2x + 8x3 + 3x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + 8x2 + 3x4) = 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 '(2 + 8x2 + 3x4)' equal to zero and attempt to solve: Simplifying 2 + 8x2 + 3x4 = 0 Solving 2 + 8x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 2.666666667x2 + x4 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 2.666666667x2 + -0.6666666667 + x4 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 2.666666667x2 + x4 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 2.666666667x2 + x4 = 0 + -0.6666666667 2.666666667x2 + x4 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 2.666666667x2 + x4 = -0.6666666667 The x term is 2.666666667x2. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x2 + 1.777777780 + x4 = -0.6666666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x2 + x4 = -0.6666666667 + 1.777777780 Combine like terms: -0.6666666667 + 1.777777780 = 1.1111111133 1.777777780 + 2.666666667x2 + x4 = 1.1111111133 Factor a perfect square on the left side: (x2 + 1.333333334)(x2 + 1.333333334) = 1.1111111133 Calculate the square root of the right side: 1.054092554 Break this problem into two subproblems by setting (x2 + 1.333333334) equal to 1.054092554 and -1.054092554.Subproblem 1
x2 + 1.333333334 = 1.054092554 Simplifying x2 + 1.333333334 = 1.054092554 Reorder the terms: 1.333333334 + x2 = 1.054092554 Solving 1.333333334 + x2 = 1.054092554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x2 = 1.054092554 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x2 = 1.054092554 + -1.333333334 x2 = 1.054092554 + -1.333333334 Combine like terms: 1.054092554 + -1.333333334 = -0.27924078 x2 = -0.27924078 Simplifying x2 = -0.27924078 Reorder the terms: 0.27924078 + x2 = -0.27924078 + 0.27924078 Combine like terms: -0.27924078 + 0.27924078 = 0.00000000 0.27924078 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 1.333333334 = -1.054092554 Simplifying x2 + 1.333333334 = -1.054092554 Reorder the terms: 1.333333334 + x2 = -1.054092554 Solving 1.333333334 + x2 = -1.054092554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x2 = -1.054092554 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x2 = -1.054092554 + -1.333333334 x2 = -1.054092554 + -1.333333334 Combine like terms: -1.054092554 + -1.333333334 = -2.387425888 x2 = -2.387425888 Simplifying x2 = -2.387425888 Reorder the terms: 2.387425888 + x2 = -2.387425888 + 2.387425888 Combine like terms: -2.387425888 + 2.387425888 = 0.000000000 2.387425888 + 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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