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Simplifying x6 + -10x4 + -24x2 = 0 Reorder the terms: -24x2 + -10x4 + x6 = 0 Solving -24x2 + -10x4 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-24 + -10x2 + x4) = 0 Factor a trinomial. x2((-2 + -1x2)(12 + -1x2)) = 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 '(-2 + -1x2)' equal to zero and attempt to solve: Simplifying -2 + -1x2 = 0 Solving -2 + -1x2 = 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 + -1x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x2 = 0 + 2 -1x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1x2 = 2 Divide each side by '-1'. x2 = -2 Simplifying x2 = -2 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 '(12 + -1x2)' equal to zero and attempt to solve: Simplifying 12 + -1x2 = 0 Solving 12 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x2 = 0 + -12 -1x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -1x2 = -12 Divide each side by '-1'. x2 = 12 Simplifying x2 = 12 Take the square root of each side: x = {-3.464101615, 3.464101615}Solution
x = {0, -3.464101615, 3.464101615}
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