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Simplifying 0 = 4x2 + -9x6 Solving 0 = 4x2 + -9x6 Solving for variable 'x'. Remove the zero: -4x2 + 9x6 = 4x2 + -9x6 + -4x2 + 9x6 Reorder the terms: -4x2 + 9x6 = 4x2 + -4x2 + -9x6 + 9x6 Combine like terms: 4x2 + -4x2 = 0 -4x2 + 9x6 = 0 + -9x6 + 9x6 -4x2 + 9x6 = -9x6 + 9x6 Combine like terms: -9x6 + 9x6 = 0 -4x2 + 9x6 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + 9x4) = 0 Factor a difference between two squares. x2((2 + 3x2)(-2 + 3x2)) = 0Subproblem 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 '(2 + 3x2)' equal to zero and attempt to solve: Simplifying 2 + 3x2 = 0 Solving 2 + 3x2 = 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 + 3x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x2 = 0 + -2 3x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3x2 = -2 Divide each side by '3'. x2 = -0.6666666667 Simplifying x2 = -0.6666666667 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-2 + 3x2)' equal to zero and attempt to solve: Simplifying -2 + 3x2 = 0 Solving -2 + 3x2 = 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 + 3x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x2 = 0 + 2 3x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3x2 = 2 Divide each side by '3'. x2 = 0.6666666667 Simplifying x2 = 0.6666666667 Take the square root of each side: x = {-0.816496581, 0.816496581}Solution
x = {0, -0.816496581, 0.816496581}
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