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Simplifying x4 + 5x2 + 5 = 0 Reorder the terms: 5 + 5x2 + x4 = 0 Solving 5 + 5x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5x2 + -5 + x4 = 0 + -5 Reorder the terms: 5 + -5 + 5x2 + x4 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5x2 + x4 = 0 + -5 5x2 + x4 = 0 + -5 Combine like terms: 0 + -5 = -5 5x2 + x4 = -5 The x term is 5x2. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x2 + 6.25 + x4 = -5 + 6.25 Reorder the terms: 6.25 + 5x2 + x4 = -5 + 6.25 Combine like terms: -5 + 6.25 = 1.25 6.25 + 5x2 + x4 = 1.25 Factor a perfect square on the left side: (x2 + 2.5)(x2 + 2.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x2 + 2.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x2 + 2.5 = 1.118033989 Simplifying x2 + 2.5 = 1.118033989 Reorder the terms: 2.5 + x2 = 1.118033989 Solving 2.5 + x2 = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = 1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = 1.118033989 + -2.5 x2 = 1.118033989 + -2.5 Combine like terms: 1.118033989 + -2.5 = -1.381966011 x2 = -1.381966011 Simplifying x2 = -1.381966011 Reorder the terms: 1.381966011 + x2 = -1.381966011 + 1.381966011 Combine like terms: -1.381966011 + 1.381966011 = 0.000000000 1.381966011 + x2 = 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
x2 + 2.5 = -1.118033989 Simplifying x2 + 2.5 = -1.118033989 Reorder the terms: 2.5 + x2 = -1.118033989 Solving 2.5 + x2 = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = -1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = -1.118033989 + -2.5 x2 = -1.118033989 + -2.5 Combine like terms: -1.118033989 + -2.5 = -3.618033989 x2 = -3.618033989 Simplifying x2 = -3.618033989 Reorder the terms: 3.618033989 + x2 = -3.618033989 + 3.618033989 Combine like terms: -3.618033989 + 3.618033989 = 0.000000000 3.618033989 + x2 = 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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