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Simplifying 2x8 + -2x6 + -80x4 = 0 Reorder the terms: -80x4 + -2x6 + 2x8 = 0 Solving -80x4 + -2x6 + 2x8 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x4'. 2x4(-40 + -1x2 + x4) = 0 Ignore the factor 2.Subproblem 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 '(-40 + -1x2 + x4)' equal to zero and attempt to solve: Simplifying -40 + -1x2 + x4 = 0 Solving -40 + -1x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -1x2 + 40 + x4 = 0 + 40 Reorder the terms: -40 + 40 + -1x2 + x4 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -1x2 + x4 = 0 + 40 -1x2 + x4 = 0 + 40 Combine like terms: 0 + 40 = 40 -1x2 + x4 = 40 The x term is -1x2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x2 + 0.25 + x4 = 40 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 0.25 + -1x2 + x4 = 40.25 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x2 + -0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x2 + -0.5 = 6.34428877 Simplifying x2 + -0.5 = 6.34428877 Reorder the terms: -0.5 + x2 = 6.34428877 Solving -0.5 + x2 = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 6.34428877 + 0.5 x2 = 6.34428877 + 0.5 Combine like terms: 6.34428877 + 0.5 = 6.84428877 x2 = 6.84428877 Simplifying x2 = 6.84428877 Take the square root of each side: x = {-2.616159164, 2.616159164}Subproblem 2
x2 + -0.5 = -6.34428877 Simplifying x2 + -0.5 = -6.34428877 Reorder the terms: -0.5 + x2 = -6.34428877 Solving -0.5 + x2 = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -6.34428877 + 0.5 x2 = -6.34428877 + 0.5 Combine like terms: -6.34428877 + 0.5 = -5.84428877 x2 = -5.84428877 Simplifying x2 = -5.84428877 Reorder the terms: 5.84428877 + x2 = -5.84428877 + 5.84428877 Combine like terms: -5.84428877 + 5.84428877 = 0.00000000 5.84428877 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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