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Simplifying 18x4 + 43x2 = 5 Reorder the terms: 43x2 + 18x4 = 5 Solving 43x2 + 18x4 = 5 Solving for variable 'x'. Reorder the terms: -5 + 43x2 + 18x4 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 43x2 + 18x4 = 0 Factor a trinomial. (-5 + -2x2)(1 + -9x2) = 0 Factor a difference between two squares. (-5 + -2x2)((1 + 3x)(1 + -3x)) = 0Subproblem 1
Set the factor '(-5 + -2x2)' equal to zero and attempt to solve: Simplifying -5 + -2x2 = 0 Solving -5 + -2x2 = 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 + -2x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x2 = 0 + 5 -2x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2x2 = 5 Divide each side by '-2'. x2 = -2.5 Simplifying x2 = -2.5 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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