F^4-5F^2=19

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Solution for F^4-5F^2=19 equation: 


Simplifying
F4 + -5F2 = 19

Reorder the terms:
-5F2 + F4 = 19

Solving
-5F2 + F4 = 19

Solving for variable 'F'.

Reorder the terms:
-19 + -5F2 + F4 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + -5F2 + F4 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -5F2 + 19 + F4 = 0 + 19

Reorder the terms:
-19 + 19 + -5F2 + F4 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -5F2 + F4 = 0 + 19
-5F2 + F4 = 0 + 19

Combine like terms: 0 + 19 = 19
-5F2 + F4 = 19

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 = 19 + 6.25

Reorder the terms:
6.25 + -5F2 + F4 = 19 + 6.25

Combine like terms: 19 + 6.25 = 25.25
6.25 + -5F2 + F4 = 25.25

Factor a perfect square on the left side:
(F2 + -2.5)(F2 + -2.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(F2 + -2.5) equal to 5.024937811 and -5.024937811.


Subproblem 1
F2 + -2.5 = 5.024937811

Simplifying
F2 + -2.5 = 5.024937811

Reorder the terms:
-2.5 + F2 = 5.024937811

Solving
-2.5 + F2 = 5.024937811

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 = 5.024937811 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + F2 = 5.024937811 + 2.5
F2 = 5.024937811 + 2.5

Combine like terms: 5.024937811 + 2.5 = 7.524937811
F2 = 7.524937811

Simplifying
F2 = 7.524937811

Take the square root of each side:
F = {-2.74316201, 2.74316201}


Subproblem 2
F2 + -2.5 = -5.024937811

Simplifying
F2 + -2.5 = -5.024937811

Reorder the terms:
-2.5 + F2 = -5.024937811

Solving
-2.5 + F2 = -5.024937811

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 = -5.024937811 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + F2 = -5.024937811 + 2.5
F2 = -5.024937811 + 2.5

Combine like terms: -5.024937811 + 2.5 = -2.524937811
F2 = -2.524937811

Simplifying
F2 = -2.524937811

Reorder the terms:
2.524937811 + F2 = -2.524937811 + 2.524937811

Combine like terms: -2.524937811 + 2.524937811 = 0.000000000
2.524937811 + 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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