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Simplifying 0 = 4x4 + 7x2 + -2 Reorder the terms: 0 = -2 + 7x2 + 4x4 Solving 0 = -2 + 7x2 + 4x4 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + -7x2 + -4x4 = -2 + 7x2 + 4x4 + 2 + -7x2 + -4x4 Reorder the terms: 2 + -7x2 + -4x4 = -2 + 2 + 7x2 + -7x2 + 4x4 + -4x4 Combine like terms: -2 + 2 = 0 2 + -7x2 + -4x4 = 0 + 7x2 + -7x2 + 4x4 + -4x4 2 + -7x2 + -4x4 = 7x2 + -7x2 + 4x4 + -4x4 Combine like terms: 7x2 + -7x2 = 0 2 + -7x2 + -4x4 = 0 + 4x4 + -4x4 2 + -7x2 + -4x4 = 4x4 + -4x4 Combine like terms: 4x4 + -4x4 = 0 2 + -7x2 + -4x4 = 0 Factor a trinomial. (1 + -4x2)(2 + x2) = 0 Factor a difference between two squares. ((1 + 2x)(1 + -2x))(2 + x2) = 0Subproblem 1
Set the factor '(2 + x2)' equal to zero and attempt to solve: Simplifying 2 + x2 = 0 Solving 2 + x2 = 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 + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 0 + -2 x2 = 0 + -2 Combine like terms: 0 + -2 = -2 x2 = -2 Simplifying x2 = -2 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 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-0.5, 0.5}
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