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Simplifying x4 + 7x2 + 5 = 0 Reorder the terms: 5 + 7x2 + x4 = 0 Solving 5 + 7x2 + 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 + 7x2 + -5 + x4 = 0 + -5 Reorder the terms: 5 + -5 + 7x2 + x4 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7x2 + x4 = 0 + -5 7x2 + x4 = 0 + -5 Combine like terms: 0 + -5 = -5 7x2 + x4 = -5 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 = -5 + 12.25 Reorder the terms: 12.25 + 7x2 + x4 = -5 + 12.25 Combine like terms: -5 + 12.25 = 7.25 12.25 + 7x2 + x4 = 7.25 Factor a perfect square on the left side: (x2 + 3.5)(x2 + 3.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x2 + 3.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x2 + 3.5 = 2.692582404 Simplifying x2 + 3.5 = 2.692582404 Reorder the terms: 3.5 + x2 = 2.692582404 Solving 3.5 + x2 = 2.692582404 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 = 2.692582404 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = 2.692582404 + -3.5 x2 = 2.692582404 + -3.5 Combine like terms: 2.692582404 + -3.5 = -0.807417596 x2 = -0.807417596 Simplifying x2 = -0.807417596 Reorder the terms: 0.807417596 + x2 = -0.807417596 + 0.807417596 Combine like terms: -0.807417596 + 0.807417596 = 0.000000000 0.807417596 + 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 = -2.692582404 Simplifying x2 + 3.5 = -2.692582404 Reorder the terms: 3.5 + x2 = -2.692582404 Solving 3.5 + x2 = -2.692582404 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 = -2.692582404 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = -2.692582404 + -3.5 x2 = -2.692582404 + -3.5 Combine like terms: -2.692582404 + -3.5 = -6.192582404 x2 = -6.192582404 Simplifying x2 = -6.192582404 Reorder the terms: 6.192582404 + x2 = -6.192582404 + 6.192582404 Combine like terms: -6.192582404 + 6.192582404 = 0.000000000 6.192582404 + 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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