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Simplifying 256x12 + x4 = 32x8 Reorder the terms: x4 + 256x12 = 32x8 Solving x4 + 256x12 = 32x8 Solving for variable 'x'. Reorder the terms: x4 + -32x8 + 256x12 = 32x8 + -32x8 Combine like terms: 32x8 + -32x8 = 0 x4 + -32x8 + 256x12 = 0 Factor out the Greatest Common Factor (GCF), 'x4'. x4(1 + -32x4 + 256x8) = 0 Factor a trinomial. x4((1 + -16x4)(1 + -16x4)) = 0 Factor a difference between two squares. x4(((1 + 4x2)(1 + -4x2))(1 + -16x4)) = 0 Factor a difference between two squares. x4(((1 + 4x2)((1 + 2x)(1 + -2x)))(1 + -16x4)) = 0 Factor a difference between two squares. x4(((1 + 4x2)(1 + -4x2))(1 + 4x2)(1 + 2x)(1 + -2x)) = 0 Factor a difference between two squares. x4(((1 + 4x2)((1 + 2x)(1 + -2x)))(1 + 4x2)(1 + 2x)(1 + -2x)) = 0Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 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 + 4x2)' equal to zero and attempt to solve: Simplifying 1 + 4x2 = 0 Solving 1 + 4x2 = 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 + 4x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x2 = 0 + -1 4x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4x2 = -1 Divide each side by '4'. x2 = -0.25 Simplifying x2 = -0.25 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 '(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 4
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 5
Set the factor '(1 + 4x2)' equal to zero and attempt to solve: Simplifying 1 + 4x2 = 0 Solving 1 + 4x2 = 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 + 4x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x2 = 0 + -1 4x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4x2 = -1 Divide each side by '4'. x2 = -0.25 Simplifying x2 = -0.25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 6
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 7
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, -0.5, 0.5}
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