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Simplifying -24x5 + 16x3 + -2x = 0 Reorder the terms: -2x + 16x3 + -24x5 = 0 Solving -2x + 16x3 + -24x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1 + 8x2 + -12x4) = 0 Factor a trinomial. 2x((-1 + 2x2)(1 + -6x2)) = 0 Ignore the factor 2.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 '(-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}Subproblem 3
Set the factor '(1 + -6x2)' equal to zero and attempt to solve: Simplifying 1 + -6x2 = 0 Solving 1 + -6x2 = 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 + -6x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x2 = 0 + -1 -6x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6x2 = -1 Divide each side by '-6'. x2 = 0.1666666667 Simplifying x2 = 0.1666666667 Take the square root of each side: x = {-0.408248291, 0.408248291}Solution
x = {0, -0.707106781, 0.707106781, -0.408248291, 0.408248291}
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