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Simplifying 0 = 6x4 + -9x2 Reorder the terms: 0 = -9x2 + 6x4 Solving 0 = -9x2 + 6x4 Solving for variable 'x'. Remove the zero: 9x2 + -6x4 = -9x2 + 6x4 + 9x2 + -6x4 Reorder the terms: 9x2 + -6x4 = -9x2 + 9x2 + 6x4 + -6x4 Combine like terms: -9x2 + 9x2 = 0 9x2 + -6x4 = 0 + 6x4 + -6x4 9x2 + -6x4 = 6x4 + -6x4 Combine like terms: 6x4 + -6x4 = 0 9x2 + -6x4 = 0 Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(3 + -2x2) = 0 Ignore the factor 3.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 '(3 + -2x2)' equal to zero and attempt to solve: Simplifying 3 + -2x2 = 0 Solving 3 + -2x2 = 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 + -2x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x2 = 0 + -3 -2x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2x2 = -3 Divide each side by '-2'. x2 = 1.5 Simplifying x2 = 1.5 Take the square root of each side: x = {-1.224744871, 1.224744871}Solution
x = {0, -1.224744871, 1.224744871}
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