1+13x^2+x^4=0

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Solution for 1+13x^2+x^4=0 equation:


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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