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Simplifying 4x5 + -1x = 0 Reorder the terms: -1x + 4x5 = 0 Solving -1x + 4x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 4x4) = 0 Factor a difference between two squares. x((1 + 2x2)(-1 + 2x2)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 2x2 = 0 Solving 1 + 2x2 = 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 + 2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x2 = 0 + -1 2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2x2 = -1 Divide each side by '2'. x2 = -0.5 Simplifying x2 = -0.5 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 + 2x2)' equal to zero and attempt to solve: Simplifying -1 + 2x2 = 0 Solving -1 + 2x2 = 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 + 2x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x2 = 0 + 1 2x2 = 0 + 1 Combine like terms: 0 + 1 = 1 2x2 = 1 Divide each side by '2'. x2 = 0.5 Simplifying x2 = 0.5 Take the square root of each side: x = {-0.707106781, 0.707106781}Solution
x = {0, -0.707106781, 0.707106781}
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