9x^4+23x^2-16=0

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Solution for 9x^4+23x^2-16=0 equation: 


Simplifying
9x4 + 23x2 + -16 = 0

Reorder the terms:
-16 + 23x2 + 9x4 = 0

Solving
-16 + 23x2 + 9x4 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-1.777777778 + 2.555555556x2 + x4 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + 2.555555556x2 + 1.777777778 + x4 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + 2.555555556x2 + x4 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + 2.555555556x2 + x4 = 0 + 1.777777778
2.555555556x2 + x4 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
2.555555556x2 + x4 = 1.777777778

The x term is 2.555555556x2.  Take half its coefficient (1.277777778).
Square it (1.632716050) and add it to both sides.

Add '1.632716050' to each side of the equation.
2.555555556x2 + 1.632716050 + x4 = 1.777777778 + 1.632716050

Reorder the terms:
1.632716050 + 2.555555556x2 + x4 = 1.777777778 + 1.632716050

Combine like terms: 1.777777778 + 1.632716050 = 3.410493828
1.632716050 + 2.555555556x2 + x4 = 3.410493828

Factor a perfect square on the left side:
(x2 + 1.277777778)(x2 + 1.277777778) = 3.410493828

Calculate the square root of the right side: 1.846752238

Break this problem into two subproblems by setting 
(x2 + 1.277777778) equal to 1.846752238 and -1.846752238.


Subproblem 1
x2 + 1.277777778 = 1.846752238

Simplifying
x2 + 1.277777778 = 1.846752238

Reorder the terms:
1.277777778 + x2 = 1.846752238

Solving
1.277777778 + x2 = 1.846752238

Solving for variable 'x'.

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

Add '-1.277777778' to each side of the equation.
1.277777778 + -1.277777778 + x2 = 1.846752238 + -1.277777778

Combine like terms: 1.277777778 + -1.277777778 = 0.000000000
0.000000000 + x2 = 1.846752238 + -1.277777778
x2 = 1.846752238 + -1.277777778

Combine like terms: 1.846752238 + -1.277777778 = 0.56897446
x2 = 0.56897446

Simplifying
x2 = 0.56897446

Take the square root of each side:
x = {-0.754303957, 0.754303957}


Subproblem 2
x2 + 1.277777778 = -1.846752238

Simplifying
x2 + 1.277777778 = -1.846752238

Reorder the terms:
1.277777778 + x2 = -1.846752238

Solving
1.277777778 + x2 = -1.846752238

Solving for variable 'x'.

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

Add '-1.277777778' to each side of the equation.
1.277777778 + -1.277777778 + x2 = -1.846752238 + -1.277777778

Combine like terms: 1.277777778 + -1.277777778 = 0.000000000
0.000000000 + x2 = -1.846752238 + -1.277777778
x2 = -1.846752238 + -1.277777778

Combine like terms: -1.846752238 + -1.277777778 = -3.124530016
x2 = -3.124530016

Simplifying
x2 = -3.124530016

Reorder the terms:
3.124530016 + x2 = -3.124530016 + 3.124530016

Combine like terms: -3.124530016 + 3.124530016 = 0.000000000
3.124530016 + 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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