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Simplifying x8 + -3x4 + 1 = 0 Reorder the terms: 1 + -3x4 + x8 = 0 Solving 1 + -3x4 + x8 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3x4 + -1 + x8 = 0 + -1 Reorder the terms: 1 + -1 + -3x4 + x8 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x4 + x8 = 0 + -1 -3x4 + x8 = 0 + -1 Combine like terms: 0 + -1 = -1 -3x4 + x8 = -1 The x term is -3x4. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x4 + 2.25 + x8 = -1 + 2.25 Reorder the terms: 2.25 + -3x4 + x8 = -1 + 2.25 Combine like terms: -1 + 2.25 = 1.25 2.25 + -3x4 + x8 = 1.25 Factor a perfect square on the left side: (x4 + -1.5)(x4 + -1.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x4 + -1.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x4 + -1.5 = 1.118033989 Simplifying x4 + -1.5 = 1.118033989 Reorder the terms: -1.5 + x4 = 1.118033989 Solving -1.5 + x4 = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x4 = 1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x4 = 1.118033989 + 1.5 x4 = 1.118033989 + 1.5 Combine like terms: 1.118033989 + 1.5 = 2.618033989 x4 = 2.618033989 Simplifying x4 = 2.618033989 Reorder the terms: -2.618033989 + x4 = 2.618033989 + -2.618033989 Combine like terms: 2.618033989 + -2.618033989 = 0.000000000 -2.618033989 + 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 + -1.5 = -1.118033989 Simplifying x4 + -1.5 = -1.118033989 Reorder the terms: -1.5 + x4 = -1.118033989 Solving -1.5 + x4 = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x4 = -1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x4 = -1.118033989 + 1.5 x4 = -1.118033989 + 1.5 Combine like terms: -1.118033989 + 1.5 = 0.381966011 x4 = 0.381966011 Simplifying x4 = 0.381966011 Reorder the terms: -0.381966011 + x4 = 0.381966011 + -0.381966011 Combine like terms: 0.381966011 + -0.381966011 = 0.000000000 -0.381966011 + 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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