7U^4+U^2=16

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Solution for 7U^4+U^2=16 equation: 


Simplifying
7U4 + U2 = 16

Reorder the terms:
U2 + 7U4 = 16

Solving
U2 + 7U4 = 16

Solving for variable 'U'.

Reorder the terms:
-16 + U2 + 7U4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + U2 + 7U4 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-2.285714286 + 0.1428571429U2 + U4 = 0

Move the constant term to the right:

Add '2.285714286' to each side of the equation.
-2.285714286 + 0.1428571429U2 + 2.285714286 + U4 = 0 + 2.285714286

Reorder the terms:
-2.285714286 + 2.285714286 + 0.1428571429U2 + U4 = 0 + 2.285714286

Combine like terms: -2.285714286 + 2.285714286 = 0.000000000
0.000000000 + 0.1428571429U2 + U4 = 0 + 2.285714286
0.1428571429U2 + U4 = 0 + 2.285714286

Combine like terms: 0 + 2.285714286 = 2.285714286
0.1428571429U2 + U4 = 2.285714286

The U term is U2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1428571429U2 + 0.25 + U4 = 2.285714286 + 0.25

Reorder the terms:
0.25 + 0.1428571429U2 + U4 = 2.285714286 + 0.25

Combine like terms: 2.285714286 + 0.25 = 2.535714286
0.25 + 0.1428571429U2 + U4 = 2.535714286

Factor a perfect square on the left side:
(U2 + 0.5)(U2 + 0.5) = 2.535714286

Calculate the square root of the right side: 1.592392629

Break this problem into two subproblems by setting 
(U2 + 0.5) equal to 1.592392629 and -1.592392629.


Subproblem 1
U2 + 0.5 = 1.592392629

Simplifying
U2 + 0.5 = 1.592392629

Reorder the terms:
0.5 + U2 = 1.592392629

Solving
0.5 + U2 = 1.592392629

Solving for variable 'U'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + U2 = 1.592392629 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + U2 = 1.592392629 + -0.5
U2 = 1.592392629 + -0.5

Combine like terms: 1.592392629 + -0.5 = 1.092392629
U2 = 1.092392629

Simplifying
U2 = 1.092392629

Take the square root of each side:
U = {-1.045175884, 1.045175884}


Subproblem 2
U2 + 0.5 = -1.592392629

Simplifying
U2 + 0.5 = -1.592392629

Reorder the terms:
0.5 + U2 = -1.592392629

Solving
0.5 + U2 = -1.592392629

Solving for variable 'U'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + U2 = -1.592392629 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + U2 = -1.592392629 + -0.5
U2 = -1.592392629 + -0.5

Combine like terms: -1.592392629 + -0.5 = -2.092392629
U2 = -2.092392629

Simplifying
U2 = -2.092392629

Reorder the terms:
2.092392629 + U2 = -2.092392629 + 2.092392629

Combine like terms: -2.092392629 + 2.092392629 = 0.000000000
2.092392629 + U2 = 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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