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Simplifying (1 + 12x2 + 36x4)(-144x) + -1(12 + -72x2)(2)(1 + 6x2)(12x) = 0 Remove parenthesis around (-144x) (1 + 12x2 + 36x4) * -144x + -1(12 + -72x2)(2)(1 + 6x2)(12x) = 0 Reorder the terms for easier multiplication: -144x(1 + 12x2 + 36x4) + -1(12 + -72x2)(2)(1 + 6x2)(12x) = 0 (1 * -144x + 12x2 * -144x + 36x4 * -144x) + -1(12 + -72x2)(2)(1 + 6x2)(12x) = 0 (-144x + -1728x3 + -5184x5) + -1(12 + -72x2)(2)(1 + 6x2)(12x) = 0 Remove parenthesis around (12x) -144x + -1728x3 + -5184x5 + -1(12 + -72x2) * 2(1 + 6x2) * 12x = 0 Reorder the terms for easier multiplication: -144x + -1728x3 + -5184x5 + -1 * 2 * 12x(12 + -72x2)(1 + 6x2) = 0 Multiply -1 * 2 -144x + -1728x3 + -5184x5 + -2 * 12x(12 + -72x2)(1 + 6x2) = 0 Multiply -2 * 12 -144x + -1728x3 + -5184x5 + -24x(12 + -72x2)(1 + 6x2) = 0 Multiply (12 + -72x2) * (1 + 6x2) -144x + -1728x3 + -5184x5 + -24x(12(1 + 6x2) + -72x2 * (1 + 6x2)) = 0 -144x + -1728x3 + -5184x5 + -24x((1 * 12 + 6x2 * 12) + -72x2 * (1 + 6x2)) = 0 -144x + -1728x3 + -5184x5 + -24x((12 + 72x2) + -72x2 * (1 + 6x2)) = 0 -144x + -1728x3 + -5184x5 + -24x(12 + 72x2 + (1 * -72x2 + 6x2 * -72x2)) = 0 -144x + -1728x3 + -5184x5 + -24x(12 + 72x2 + (-72x2 + -432x4)) = 0 Combine like terms: 72x2 + -72x2 = 0 -144x + -1728x3 + -5184x5 + -24x(12 + 0 + -432x4) = 0 -144x + -1728x3 + -5184x5 + -24x(12 + -432x4) = 0 -144x + -1728x3 + -5184x5 + (12 * -24x + -432x4 * -24x) = 0 -144x + -1728x3 + -5184x5 + (-288x + 10368x5) = 0 Reorder the terms: -144x + -288x + -1728x3 + -5184x5 + 10368x5 = 0 Combine like terms: -144x + -288x = -432x -432x + -1728x3 + -5184x5 + 10368x5 = 0 Combine like terms: -5184x5 + 10368x5 = 5184x5 -432x + -1728x3 + 5184x5 = 0 Solving -432x + -1728x3 + 5184x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '432x'. 432x(-1 + -4x2 + 12x4) = 0 Factor a trinomial. 432x((-1 + -6x2)(1 + -2x2)) = 0 Ignore the factor 432.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 + -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 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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