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Simplifying 27x4 + 60x2 = 32 Reorder the terms: 60x2 + 27x4 = 32 Solving 60x2 + 27x4 = 32 Solving for variable 'x'. Reorder the terms: -32 + 60x2 + 27x4 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 60x2 + 27x4 = 0 Factor a trinomial. (-8 + -3x2)(4 + -9x2) = 0 Factor a difference between two squares. (-8 + -3x2)((2 + 3x)(2 + -3x)) = 0Subproblem 1
Set the factor '(-8 + -3x2)' equal to zero and attempt to solve: Simplifying -8 + -3x2 = 0 Solving -8 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3x2 = 0 + 8 -3x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3x2 = 8 Divide each side by '-3'. x2 = -2.666666667 Simplifying x2 = -2.666666667 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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 3
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-0.6666666667, 0.6666666667}
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