0=9x^4-3x^2-7

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Solution for 0=9x^4-3x^2-7 equation: 


Simplifying
0 = 9x4 + -3x2 + -7

Reorder the terms:
0 = -7 + -3x2 + 9x4

Solving
0 = -7 + -3x2 + 9x4

Solving for variable 'x'.

Combine like terms: 0 + 7 = 7
7 + 3x2 + -9x4 = -7 + -3x2 + 9x4 + 7 + 3x2 + -9x4

Reorder the terms:
7 + 3x2 + -9x4 = -7 + 7 + -3x2 + 3x2 + 9x4 + -9x4

Combine like terms: -7 + 7 = 0
7 + 3x2 + -9x4 = 0 + -3x2 + 3x2 + 9x4 + -9x4
7 + 3x2 + -9x4 = -3x2 + 3x2 + 9x4 + -9x4

Combine like terms: -3x2 + 3x2 = 0
7 + 3x2 + -9x4 = 0 + 9x4 + -9x4
7 + 3x2 + -9x4 = 9x4 + -9x4

Combine like terms: 9x4 + -9x4 = 0
7 + 3x2 + -9x4 = 0

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

Divide each side by '-9'.
-0.7777777778 + -0.3333333333x2 + x4 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + -0.3333333333x2 + 0.7777777778 + x4 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + -0.3333333333x2 + x4 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + -0.3333333333x2 + x4 = 0 + 0.7777777778
-0.3333333333x2 + x4 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
-0.3333333333x2 + x4 = 0.7777777778

The x term is -0.3333333333x2.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x2 + 0.02777777779 + x4 = 0.7777777778 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x2 + x4 = 0.7777777778 + 0.02777777779

Combine like terms: 0.7777777778 + 0.02777777779 = 0.80555555559
0.02777777779 + -0.3333333333x2 + x4 = 0.80555555559

Factor a perfect square on the left side:
(x2 + -0.1666666667)(x2 + -0.1666666667) = 0.80555555559

Calculate the square root of the right side: 0.897527468

Break this problem into two subproblems by setting 
(x2 + -0.1666666667) equal to 0.897527468 and -0.897527468.


Subproblem 1
x2 + -0.1666666667 = 0.897527468

Simplifying
x2 + -0.1666666667 = 0.897527468

Reorder the terms:
-0.1666666667 + x2 = 0.897527468

Solving
-0.1666666667 + x2 = 0.897527468

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x2 = 0.897527468 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x2 = 0.897527468 + 0.1666666667
x2 = 0.897527468 + 0.1666666667

Combine like terms: 0.897527468 + 0.1666666667 = 1.0641941347
x2 = 1.0641941347

Simplifying
x2 = 1.0641941347

Take the square root of each side:
x = {-1.031597855, 1.031597855}


Subproblem 2
x2 + -0.1666666667 = -0.897527468

Simplifying
x2 + -0.1666666667 = -0.897527468

Reorder the terms:
-0.1666666667 + x2 = -0.897527468

Solving
-0.1666666667 + x2 = -0.897527468

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x2 = -0.897527468 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x2 = -0.897527468 + 0.1666666667
x2 = -0.897527468 + 0.1666666667

Combine like terms: -0.897527468 + 0.1666666667 = -0.7308608013
x2 = -0.7308608013

Simplifying
x2 = -0.7308608013

Reorder the terms:
0.7308608013 + x2 = -0.7308608013 + 0.7308608013

Combine like terms: -0.7308608013 + 0.7308608013 = 0.0000000000
0.7308608013 + x2 = 0.0000000000

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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