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Simplifying 12x6 + -5x4 + -25x2 = 0 Reorder the terms: -25x2 + -5x4 + 12x6 = 0 Solving -25x2 + -5x4 + 12x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-25 + -5x2 + 12x4) = 0 Factor a trinomial. x2((-5 + -4x2)(5 + -3x2)) = 0Subproblem 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 '(-5 + -4x2)' equal to zero and attempt to solve: Simplifying -5 + -4x2 = 0 Solving -5 + -4x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -4x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x2 = 0 + 5 -4x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4x2 = 5 Divide each side by '-4'. x2 = -1.25 Simplifying x2 = -1.25 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 '(5 + -3x2)' equal to zero and attempt to solve: Simplifying 5 + -3x2 = 0 Solving 5 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x2 = 0 + -5 -3x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3x2 = -5 Divide each side by '-3'. x2 = 1.666666667 Simplifying x2 = 1.666666667 Take the square root of each side: x = {-1.290994449, 1.290994449}Solution
x = {0, -1.290994449, 1.290994449}
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