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Simplifying 6x6 + -14x4 + -12x2 = 0 Reorder the terms: -12x2 + -14x4 + 6x6 = 0 Solving -12x2 + -14x4 + 6x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-6 + -7x2 + 3x4) = 0 Factor a trinomial. 2x2((-2 + -3x2)(3 + -1x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-2 + -3x2)' equal to zero and attempt to solve: Simplifying -2 + -3x2 = 0 Solving -2 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x2 = 0 + 2 -3x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3x2 = 2 Divide each side by '-3'. x2 = -0.6666666667 Simplifying x2 = -0.6666666667 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 '(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}Solution
x = {0, -1.732050808, 1.732050808}
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