1+12x^2+x^4=0

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Solution for 1+12x^2+x^4=0 equation:


Simplifying
1 + 12x2 + x4 = 0

Solving
1 + 12x2 + 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 + 12x2 + -1 + x4 = 0 + -1

Reorder the terms:
1 + -1 + 12x2 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12x2 + x4 = 0 + -1
12x2 + x4 = 0 + -1

Combine like terms: 0 + -1 = -1
12x2 + x4 = -1

The x term is 12x2.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x2 + 36 + x4 = -1 + 36

Reorder the terms:
36 + 12x2 + x4 = -1 + 36

Combine like terms: -1 + 36 = 35
36 + 12x2 + x4 = 35

Factor a perfect square on the left side:
(x2 + 6)(x2 + 6) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(x2 + 6) equal to 5.916079783 and -5.916079783.

Subproblem 1

x2 + 6 = 5.916079783 Simplifying x2 + 6 = 5.916079783 Reorder the terms: 6 + x2 = 5.916079783 Solving 6 + x2 = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = 5.916079783 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 5.916079783 + -6 x2 = 5.916079783 + -6 Combine like terms: 5.916079783 + -6 = -0.083920217 x2 = -0.083920217 Simplifying x2 = -0.083920217 Reorder the terms: 0.083920217 + x2 = -0.083920217 + 0.083920217 Combine like terms: -0.083920217 + 0.083920217 = 0.000000000 0.083920217 + 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 = -5.916079783 Simplifying x2 + 6 = -5.916079783 Reorder the terms: 6 + x2 = -5.916079783 Solving 6 + x2 = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = -5.916079783 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = -5.916079783 + -6 x2 = -5.916079783 + -6 Combine like terms: -5.916079783 + -6 = -11.916079783 x2 = -11.916079783 Simplifying x2 = -11.916079783 Reorder the terms: 11.916079783 + x2 = -11.916079783 + 11.916079783 Combine like terms: -11.916079783 + 11.916079783 = 0.000000000 11.916079783 + 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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