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

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


Simplifying
4x4 + 3x2 + -9 = 0

Reorder the terms:
-9 + 3x2 + 4x4 = 0

Solving
-9 + 3x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-2.25 + 0.75x2 + x4 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 0.75x2 + 2.25 + x4 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 0.75x2 + x4 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 0.75x2 + x4 = 0 + 2.25
0.75x2 + x4 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
0.75x2 + x4 = 2.25

The x term is 0.75x2.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x2 + 0.140625 + x4 = 2.25 + 0.140625

Reorder the terms:
0.140625 + 0.75x2 + x4 = 2.25 + 0.140625

Combine like terms: 2.25 + 0.140625 = 2.390625
0.140625 + 0.75x2 + x4 = 2.390625

Factor a perfect square on the left side:
(x2 + 0.375)(x2 + 0.375) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(x2 + 0.375) equal to 1.54616461 and -1.54616461.


Subproblem 1
x2 + 0.375 = 1.54616461

Simplifying
x2 + 0.375 = 1.54616461

Reorder the terms:
0.375 + x2 = 1.54616461

Solving
0.375 + x2 = 1.54616461

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x2 = 1.54616461 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x2 = 1.54616461 + -0.375
x2 = 1.54616461 + -0.375

Combine like terms: 1.54616461 + -0.375 = 1.17116461
x2 = 1.17116461

Simplifying
x2 = 1.17116461

Take the square root of each side:
x = {-1.08220359, 1.08220359}


Subproblem 2
x2 + 0.375 = -1.54616461

Simplifying
x2 + 0.375 = -1.54616461

Reorder the terms:
0.375 + x2 = -1.54616461

Solving
0.375 + x2 = -1.54616461

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x2 = -1.54616461 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x2 = -1.54616461 + -0.375
x2 = -1.54616461 + -0.375

Combine like terms: -1.54616461 + -0.375 = -1.92116461
x2 = -1.92116461

Simplifying
x2 = -1.92116461

Reorder the terms:
1.92116461 + x2 = -1.92116461 + 1.92116461

Combine like terms: -1.92116461 + 1.92116461 = 0.00000000
1.92116461 + x2 = 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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