4x^4+9x^2-225=0

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Solution for 4x^4+9x^2-225=0 equation: 


Simplifying
4x4 + 9x2 + -225 = 0

Reorder the terms:
-225 + 9x2 + 4x4 = 0

Solving
-225 + 9x2 + 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'.
-56.25 + 2.25x2 + x4 = 0

Move the constant term to the right:

Add '56.25' to each side of the equation.
-56.25 + 2.25x2 + 56.25 + x4 = 0 + 56.25

Reorder the terms:
-56.25 + 56.25 + 2.25x2 + x4 = 0 + 56.25

Combine like terms: -56.25 + 56.25 = 0.00
0.00 + 2.25x2 + x4 = 0 + 56.25
2.25x2 + x4 = 0 + 56.25

Combine like terms: 0 + 56.25 = 56.25
2.25x2 + x4 = 56.25

The x term is 2.25x2.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x2 + 1.265625 + x4 = 56.25 + 1.265625

Reorder the terms:
1.265625 + 2.25x2 + x4 = 56.25 + 1.265625

Combine like terms: 56.25 + 1.265625 = 57.515625
1.265625 + 2.25x2 + x4 = 57.515625

Factor a perfect square on the left side:
(x2 + 1.125)(x2 + 1.125) = 57.515625

Calculate the square root of the right side: 7.583905656

Break this problem into two subproblems by setting 
(x2 + 1.125) equal to 7.583905656 and -7.583905656.


Subproblem 1
x2 + 1.125 = 7.583905656

Simplifying
x2 + 1.125 = 7.583905656

Reorder the terms:
1.125 + x2 = 7.583905656

Solving
1.125 + x2 = 7.583905656

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x2 = 7.583905656 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x2 = 7.583905656 + -1.125
x2 = 7.583905656 + -1.125

Combine like terms: 7.583905656 + -1.125 = 6.458905656
x2 = 6.458905656

Simplifying
x2 = 6.458905656

Take the square root of each side:
x = {-2.541437714, 2.541437714}


Subproblem 2
x2 + 1.125 = -7.583905656

Simplifying
x2 + 1.125 = -7.583905656

Reorder the terms:
1.125 + x2 = -7.583905656

Solving
1.125 + x2 = -7.583905656

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x2 = -7.583905656 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x2 = -7.583905656 + -1.125
x2 = -7.583905656 + -1.125

Combine like terms: -7.583905656 + -1.125 = -8.708905656
x2 = -8.708905656

Simplifying
x2 = -8.708905656

Reorder the terms:
8.708905656 + x2 = -8.708905656 + 8.708905656

Combine like terms: -8.708905656 + 8.708905656 = 0.000000000
8.708905656 + 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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