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Simplifying x8 + x4 = 1 Reorder the terms: x4 + x8 = 1 Solving x4 + x8 = 1 Solving for variable 'x'. Reorder the terms: -1 + x4 + x8 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + x4 + x8 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + x4 + 1 + x8 = 0 + 1 Reorder the terms: -1 + 1 + x4 + x8 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x4 + x8 = 0 + 1 x4 + x8 = 0 + 1 Combine like terms: 0 + 1 = 1 x4 + x8 = 1 The x term is x4. 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. x4 + 0.25 + x8 = 1 + 0.25 Reorder the terms: 0.25 + x4 + x8 = 1 + 0.25 Combine like terms: 1 + 0.25 = 1.25 0.25 + x4 + x8 = 1.25 Factor a perfect square on the left side: (x4 + 0.5)(x4 + 0.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x4 + 0.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x4 + 0.5 = 1.118033989 Simplifying x4 + 0.5 = 1.118033989 Reorder the terms: 0.5 + x4 = 1.118033989 Solving 0.5 + x4 = 1.118033989 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 + x4 = 1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x4 = 1.118033989 + -0.5 x4 = 1.118033989 + -0.5 Combine like terms: 1.118033989 + -0.5 = 0.618033989 x4 = 0.618033989 Simplifying x4 = 0.618033989 Reorder the terms: -0.618033989 + x4 = 0.618033989 + -0.618033989 Combine like terms: 0.618033989 + -0.618033989 = 0.000000000 -0.618033989 + x4 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x4 + 0.5 = -1.118033989 Simplifying x4 + 0.5 = -1.118033989 Reorder the terms: 0.5 + x4 = -1.118033989 Solving 0.5 + x4 = -1.118033989 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 + x4 = -1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x4 = -1.118033989 + -0.5 x4 = -1.118033989 + -0.5 Combine like terms: -1.118033989 + -0.5 = -1.618033989 x4 = -1.618033989 Simplifying x4 = -1.618033989 Reorder the terms: 1.618033989 + x4 = -1.618033989 + 1.618033989 Combine like terms: -1.618033989 + 1.618033989 = 0.000000000 1.618033989 + x4 = 0.000000000 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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