2x^4+3x^2-30=0

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Solution for 2x^4+3x^2-30=0 equation: 


Simplifying
2x4 + 3x2 + -30 = 0

Reorder the terms:
-30 + 3x2 + 2x4 = 0

Solving
-30 + 3x2 + 2x4 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-15 + 1.5x2 + x4 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 1.5x2 + 15 + x4 = 0 + 15

Reorder the terms:
-15 + 15 + 1.5x2 + x4 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 1.5x2 + x4 = 0 + 15
1.5x2 + x4 = 0 + 15

Combine like terms: 0 + 15 = 15
1.5x2 + x4 = 15

The x term is 1.5x2.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x2 + 0.5625 + x4 = 15 + 0.5625

Reorder the terms:
0.5625 + 1.5x2 + x4 = 15 + 0.5625

Combine like terms: 15 + 0.5625 = 15.5625
0.5625 + 1.5x2 + x4 = 15.5625

Factor a perfect square on the left side:
(x2 + 0.75)(x2 + 0.75) = 15.5625

Calculate the square root of the right side: 3.94493346

Break this problem into two subproblems by setting 
(x2 + 0.75) equal to 3.94493346 and -3.94493346.


Subproblem 1
x2 + 0.75 = 3.94493346

Simplifying
x2 + 0.75 = 3.94493346

Reorder the terms:
0.75 + x2 = 3.94493346

Solving
0.75 + x2 = 3.94493346

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x2 = 3.94493346 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x2 = 3.94493346 + -0.75
x2 = 3.94493346 + -0.75

Combine like terms: 3.94493346 + -0.75 = 3.19493346
x2 = 3.19493346

Simplifying
x2 = 3.19493346

Take the square root of each side:
x = {-1.78743768, 1.78743768}


Subproblem 2
x2 + 0.75 = -3.94493346

Simplifying
x2 + 0.75 = -3.94493346

Reorder the terms:
0.75 + x2 = -3.94493346

Solving
0.75 + x2 = -3.94493346

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x2 = -3.94493346 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x2 = -3.94493346 + -0.75
x2 = -3.94493346 + -0.75

Combine like terms: -3.94493346 + -0.75 = -4.69493346
x2 = -4.69493346

Simplifying
x2 = -4.69493346

Reorder the terms:
4.69493346 + x2 = -4.69493346 + 4.69493346

Combine like terms: -4.69493346 + 4.69493346 = 0.00000000
4.69493346 + 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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