F^4+5F^2=2

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Solution for F^4+5F^2=2 equation: 


Simplifying
F4 + 5F2 = 2

Reorder the terms:
5F2 + F4 = 2

Solving
5F2 + F4 = 2

Solving for variable 'F'.

Reorder the terms:
-2 + 5F2 + F4 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 5F2 + F4 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 5F2 + 2 + F4 = 0 + 2

Reorder the terms:
-2 + 2 + 5F2 + F4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5F2 + F4 = 0 + 2
5F2 + F4 = 0 + 2

Combine like terms: 0 + 2 = 2
5F2 + F4 = 2

The F term is 5F2.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5F2 + 6.25 + F4 = 2 + 6.25

Reorder the terms:
6.25 + 5F2 + F4 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + 5F2 + F4 = 8.25

Factor a perfect square on the left side:
(F2 + 2.5)(F2 + 2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(F2 + 2.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
F2 + 2.5 = 2.872281323

Simplifying
F2 + 2.5 = 2.872281323

Reorder the terms:
2.5 + F2 = 2.872281323

Solving
2.5 + F2 = 2.872281323

Solving for variable 'F'.

Move all terms containing F to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + F2 = 2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + F2 = 2.872281323 + -2.5
F2 = 2.872281323 + -2.5

Combine like terms: 2.872281323 + -2.5 = 0.372281323
F2 = 0.372281323

Simplifying
F2 = 0.372281323

Take the square root of each side:
F = {-0.610148607, 0.610148607}


Subproblem 2
F2 + 2.5 = -2.872281323

Simplifying
F2 + 2.5 = -2.872281323

Reorder the terms:
2.5 + F2 = -2.872281323

Solving
2.5 + F2 = -2.872281323

Solving for variable 'F'.

Move all terms containing F to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + F2 = -2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + F2 = -2.872281323 + -2.5
F2 = -2.872281323 + -2.5

Combine like terms: -2.872281323 + -2.5 = -5.372281323
F2 = -5.372281323

Simplifying
F2 = -5.372281323

Reorder the terms:
5.372281323 + F2 = -5.372281323 + 5.372281323

Combine like terms: -5.372281323 + 5.372281323 = 0.000000000
5.372281323 + F2 = 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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