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Simplifying 2x4 + 6x2 + 2 = 0 Reorder the terms: 2 + 6x2 + 2x4 = 0 Solving 2 + 6x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 3x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 3x2 + x4)' equal to zero and attempt to solve: Simplifying 1 + 3x2 + x4 = 0 Solving 1 + 3x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 3x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x2 + x4 = 0 + -1 3x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 3x2 + x4 = -1 The x term is 3x2. 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. 3x2 + 2.25 + x4 = -1 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = -1 + 2.25 Combine like terms: -1 + 2.25 = 1.25 2.25 + 3x2 + x4 = 1.25 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x2 + 1.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x2 + 1.5 = 1.118033989 Simplifying x2 + 1.5 = 1.118033989 Reorder the terms: 1.5 + x2 = 1.118033989 Solving 1.5 + x2 = 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 + x2 = 1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 1.118033989 + -1.5 x2 = 1.118033989 + -1.5 Combine like terms: 1.118033989 + -1.5 = -0.381966011 x2 = -0.381966011 Simplifying x2 = -0.381966011 Reorder the terms: 0.381966011 + x2 = -0.381966011 + 0.381966011 Combine like terms: -0.381966011 + 0.381966011 = 0.000000000 0.381966011 + 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 + 1.5 = -1.118033989 Simplifying x2 + 1.5 = -1.118033989 Reorder the terms: 1.5 + x2 = -1.118033989 Solving 1.5 + x2 = -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 + x2 = -1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -1.118033989 + -1.5 x2 = -1.118033989 + -1.5 Combine like terms: -1.118033989 + -1.5 = -2.618033989 x2 = -2.618033989 Simplifying x2 = -2.618033989 Reorder the terms: 2.618033989 + x2 = -2.618033989 + 2.618033989 Combine like terms: -2.618033989 + 2.618033989 = 0.000000000 2.618033989 + 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. 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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