x^4(9x^4-13)=4

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Solution for x^4(9x^4-13)=4 equation: 


Simplifying
x4(9x4 + -13) = 4

Reorder the terms:
x4(-13 + 9x4) = 4
(-13 * x4 + 9x4 * x4) = 4
(-13x4 + 9x8) = 4

Solving
-13x4 + 9x8 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -13x4 + 9x8 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -13x4 + 9x8 = 0

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

Divide each side by '9'.
-0.4444444444 + -1.444444444x4 + x8 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -1.444444444x4 + 0.4444444444 + x8 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -1.444444444x4 + x8 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -1.444444444x4 + x8 = 0 + 0.4444444444
-1.444444444x4 + x8 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-1.444444444x4 + x8 = 0.4444444444

The x term is -1.444444444x4.  Take half its coefficient (-0.722222222).
Square it (0.5216049380) and add it to both sides.

Add '0.5216049380' to each side of the equation.
-1.444444444x4 + 0.5216049380 + x8 = 0.4444444444 + 0.5216049380

Reorder the terms:
0.5216049380 + -1.444444444x4 + x8 = 0.4444444444 + 0.5216049380

Combine like terms: 0.4444444444 + 0.5216049380 = 0.9660493824
0.5216049380 + -1.444444444x4 + x8 = 0.9660493824

Factor a perfect square on the left side:
(x4 + -0.722222222)(x4 + -0.722222222) = 0.9660493824

Calculate the square root of the right side: 0.982878112

Break this problem into two subproblems by setting 
(x4 + -0.722222222) equal to 0.982878112 and -0.982878112.


Subproblem 1
x4 + -0.722222222 = 0.982878112

Simplifying
x4 + -0.722222222 = 0.982878112

Reorder the terms:
-0.722222222 + x4 = 0.982878112

Solving
-0.722222222 + x4 = 0.982878112

Solving for variable 'x'.

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

Add '0.722222222' to each side of the equation.
-0.722222222 + 0.722222222 + x4 = 0.982878112 + 0.722222222

Combine like terms: -0.722222222 + 0.722222222 = 0.000000000
0.000000000 + x4 = 0.982878112 + 0.722222222
x4 = 0.982878112 + 0.722222222

Combine like terms: 0.982878112 + 0.722222222 = 1.705100334
x4 = 1.705100334

Simplifying
x4 = 1.705100334

Reorder the terms:
-1.705100334 + x4 = 1.705100334 + -1.705100334

Combine like terms: 1.705100334 + -1.705100334 = 0.000000000
-1.705100334 + x4 = 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
x4 + -0.722222222 = -0.982878112

Simplifying
x4 + -0.722222222 = -0.982878112

Reorder the terms:
-0.722222222 + x4 = -0.982878112

Solving
-0.722222222 + x4 = -0.982878112

Solving for variable 'x'.

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

Add '0.722222222' to each side of the equation.
-0.722222222 + 0.722222222 + x4 = -0.982878112 + 0.722222222

Combine like terms: -0.722222222 + 0.722222222 = 0.000000000
0.000000000 + x4 = -0.982878112 + 0.722222222
x4 = -0.982878112 + 0.722222222

Combine like terms: -0.982878112 + 0.722222222 = -0.26065589
x4 = -0.26065589

Simplifying
x4 = -0.26065589

Reorder the terms:
0.26065589 + x4 = -0.26065589 + 0.26065589

Combine like terms: -0.26065589 + 0.26065589 = 0.00000000
0.26065589 + x4 = 0.00000000

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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