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Simplifying (-3x4 + -1) + -1(6x4 + 6x2 + -4) = 0 Reorder the terms: (-1 + -3x4) + -1(6x4 + 6x2 + -4) = 0 Remove parenthesis around (-1 + -3x4) -1 + -3x4 + -1(6x4 + 6x2 + -4) = 0 Reorder the terms: -1 + -3x4 + -1(-4 + 6x2 + 6x4) = 0 -1 + -3x4 + (-4 * -1 + 6x2 * -1 + 6x4 * -1) = 0 -1 + -3x4 + (4 + -6x2 + -6x4) = 0 Reorder the terms: -1 + 4 + -6x2 + -3x4 + -6x4 = 0 Combine like terms: -1 + 4 = 3 3 + -6x2 + -3x4 + -6x4 = 0 Combine like terms: -3x4 + -6x4 = -9x4 3 + -6x2 + -9x4 = 0 Solving 3 + -6x2 + -9x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -2x2 + -3x4) = 0 Factor a trinomial. 3((1 + -3x2)(1 + x2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -3x2)' equal to zero and attempt to solve: Simplifying 1 + -3x2 = 0 Solving 1 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x2 = 0 + -1 -3x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3x2 = -1 Divide each side by '-3'. x2 = 0.3333333333 Simplifying x2 = 0.3333333333 Take the square root of each side: x = {-0.577350269, 0.577350269}Subproblem 2
Set the factor '(1 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {-0.577350269, 0.577350269}
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