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Simplifying 1 + 13x2 + x4 = 0 Solving 1 + 13x2 + x4 = 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 + 13x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 13x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 13x2 + x4 = 0 + -1 13x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 13x2 + x4 = -1 The x term is 13x2. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x2 + 42.25 + x4 = -1 + 42.25 Reorder the terms: 42.25 + 13x2 + x4 = -1 + 42.25 Combine like terms: -1 + 42.25 = 41.25 42.25 + 13x2 + x4 = 41.25 Factor a perfect square on the left side: (x2 + 6.5)(x2 + 6.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x2 + 6.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x2 + 6.5 = 6.422616289 Simplifying x2 + 6.5 = 6.422616289 Reorder the terms: 6.5 + x2 = 6.422616289 Solving 6.5 + x2 = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x2 = 6.422616289 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x2 = 6.422616289 + -6.5 x2 = 6.422616289 + -6.5 Combine like terms: 6.422616289 + -6.5 = -0.077383711 x2 = -0.077383711 Simplifying x2 = -0.077383711 Reorder the terms: 0.077383711 + x2 = -0.077383711 + 0.077383711 Combine like terms: -0.077383711 + 0.077383711 = 0.000000000 0.077383711 + 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 + 6.5 = -6.422616289 Simplifying x2 + 6.5 = -6.422616289 Reorder the terms: 6.5 + x2 = -6.422616289 Solving 6.5 + x2 = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x2 = -6.422616289 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x2 = -6.422616289 + -6.5 x2 = -6.422616289 + -6.5 Combine like terms: -6.422616289 + -6.5 = -12.922616289 x2 = -12.922616289 Simplifying x2 = -12.922616289 Reorder the terms: 12.922616289 + x2 = -12.922616289 + 12.922616289 Combine like terms: -12.922616289 + 12.922616289 = 0.000000000 12.922616289 + 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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