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Simplifying 3x5 + -27x3 + 54x = 0 Reorder the terms: 54x + -27x3 + 3x5 = 0 Solving 54x + -27x3 + 3x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(18 + -9x2 + x4) = 0 Factor a trinomial. 3x((3 + -1x2)(6 + -1x2)) = 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 + -1x2)' equal to zero and attempt to solve: Simplifying 3 + -1x2 = 0 Solving 3 + -1x2 = 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 + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x2 = 0 + -3 -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1x2 = -3 Divide each side by '-1'. x2 = 3 Simplifying x2 = 3 Take the square root of each side: x = {-1.732050808, 1.732050808}Subproblem 3
Set the factor '(6 + -1x2)' equal to zero and attempt to solve: Simplifying 6 + -1x2 = 0 Solving 6 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x2 = 0 + -6 -1x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1x2 = -6 Divide each side by '-1'. x2 = 6 Simplifying x2 = 6 Take the square root of each side: x = {-2.449489743, 2.449489743}Solution
x = {0, -1.732050808, 1.732050808, -2.449489743, 2.449489743}
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