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Simplifying -1x4 + -7x2 + -1 = 0 Reorder the terms: -1 + -7x2 + -1x4 = 0 Solving -1 + -7x2 + -1x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 7x2 + x4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 7x2 + x4)' equal to zero and attempt to solve: Simplifying 1 + 7x2 + x4 = 0 Solving 1 + 7x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 7x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 7x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7x2 + x4 = 0 + -1 7x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 7x2 + x4 = -1 The x term is 7x2. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x2 + 12.25 + x4 = -1 + 12.25 Reorder the terms: 12.25 + 7x2 + x4 = -1 + 12.25 Combine like terms: -1 + 12.25 = 11.25 12.25 + 7x2 + x4 = 11.25 Factor a perfect square on the left side: (x2 + 3.5)(x2 + 3.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x2 + 3.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x2 + 3.5 = 3.354101966 Simplifying x2 + 3.5 = 3.354101966 Reorder the terms: 3.5 + x2 = 3.354101966 Solving 3.5 + x2 = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = 3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = 3.354101966 + -3.5 x2 = 3.354101966 + -3.5 Combine like terms: 3.354101966 + -3.5 = -0.145898034 x2 = -0.145898034 Simplifying x2 = -0.145898034 Reorder the terms: 0.145898034 + x2 = -0.145898034 + 0.145898034 Combine like terms: -0.145898034 + 0.145898034 = 0.000000000 0.145898034 + 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 + 3.5 = -3.354101966 Simplifying x2 + 3.5 = -3.354101966 Reorder the terms: 3.5 + x2 = -3.354101966 Solving 3.5 + x2 = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = -3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = -3.354101966 + -3.5 x2 = -3.354101966 + -3.5 Combine like terms: -3.354101966 + -3.5 = -6.854101966 x2 = -6.854101966 Simplifying x2 = -6.854101966 Reorder the terms: 6.854101966 + x2 = -6.854101966 + 6.854101966 Combine like terms: -6.854101966 + 6.854101966 = 0.000000000 6.854101966 + 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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