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Simplifying (15x5 + -5x3 + 2x) + (-5x5 + 6x3 + -5x) = 0 Reorder the terms: (2x + -5x3 + 15x5) + (-5x5 + 6x3 + -5x) = 0 Remove parenthesis around (2x + -5x3 + 15x5) 2x + -5x3 + 15x5 + (-5x5 + 6x3 + -5x) = 0 Reorder the terms: 2x + -5x3 + 15x5 + (-5x + 6x3 + -5x5) = 0 Remove parenthesis around (-5x + 6x3 + -5x5) 2x + -5x3 + 15x5 + -5x + 6x3 + -5x5 = 0 Reorder the terms: 2x + -5x + -5x3 + 6x3 + 15x5 + -5x5 = 0 Combine like terms: 2x + -5x = -3x -3x + -5x3 + 6x3 + 15x5 + -5x5 = 0 Combine like terms: -5x3 + 6x3 = 1x3 -3x + 1x3 + 15x5 + -5x5 = 0 Combine like terms: 15x5 + -5x5 = 10x5 -3x + 1x3 + 10x5 = 0 Solving -3x + 1x3 + 10x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + x2 + 10x4) = 0 Factor a trinomial. x((-3 + -5x2)(1 + -2x2)) = 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 '(-3 + -5x2)' equal to zero and attempt to solve: Simplifying -3 + -5x2 = 0 Solving -3 + -5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5x2 = 0 + 3 -5x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5x2 = 3 Divide each side by '-5'. x2 = -0.6 Simplifying x2 = -0.6 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -2x2)' equal to zero and attempt to solve: Simplifying 1 + -2x2 = 0 Solving 1 + -2x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x2 = 0 + -1 -2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2x2 = -1 Divide each side by '-2'. x2 = 0.5 Simplifying x2 = 0.5 Take the square root of each side: x = {-0.707106781, 0.707106781}Solution
x = {0, -0.707106781, 0.707106781}
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