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Simplifying (3x2 + 1)(9x2 + -1) = 0 Reorder the terms: (1 + 3x2)(9x2 + -1) = 0 Reorder the terms: (1 + 3x2)(-1 + 9x2) = 0 Multiply (1 + 3x2) * (-1 + 9x2) (1(-1 + 9x2) + 3x2 * (-1 + 9x2)) = 0 ((-1 * 1 + 9x2 * 1) + 3x2 * (-1 + 9x2)) = 0 ((-1 + 9x2) + 3x2 * (-1 + 9x2)) = 0 (-1 + 9x2 + (-1 * 3x2 + 9x2 * 3x2)) = 0 (-1 + 9x2 + (-3x2 + 27x4)) = 0 Combine like terms: 9x2 + -3x2 = 6x2 (-1 + 6x2 + 27x4) = 0 Solving -1 + 6x2 + 27x4 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -3x2)(1 + -9x2) = 0 Factor a difference between two squares. (-1 + -3x2)((1 + 3x)(1 + -3x)) = 0Subproblem 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 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 3
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-0.3333333333, 0.3333333333}
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