900x^2+25x^4=16

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Solution for 900x^2+25x^4=16 equation: 


Simplifying
900x2 + 25x4 = 16

Solving
900x2 + 25x4 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 900x2 + 25x4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 900x2 + 25x4 = 0

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

Divide each side by '25'.
-0.64 + 36x2 + x4 = 0

Move the constant term to the right:

Add '0.64' to each side of the equation.
-0.64 + 36x2 + 0.64 + x4 = 0 + 0.64

Reorder the terms:
-0.64 + 0.64 + 36x2 + x4 = 0 + 0.64

Combine like terms: -0.64 + 0.64 = 0.00
0.00 + 36x2 + x4 = 0 + 0.64
36x2 + x4 = 0 + 0.64

Combine like terms: 0 + 0.64 = 0.64
36x2 + x4 = 0.64

The x term is 36x2.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x2 + 324 + x4 = 0.64 + 324

Reorder the terms:
324 + 36x2 + x4 = 0.64 + 324

Combine like terms: 0.64 + 324 = 324.64
324 + 36x2 + x4 = 324.64

Factor a perfect square on the left side:
(x2 + 18)(x2 + 18) = 324.64

Calculate the square root of the right side: 18.017769007

Break this problem into two subproblems by setting 
(x2 + 18) equal to 18.017769007 and -18.017769007.


Subproblem 1
x2 + 18 = 18.017769007

Simplifying
x2 + 18 = 18.017769007

Reorder the terms:
18 + x2 = 18.017769007

Solving
18 + x2 = 18.017769007

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x2 = 18.017769007 + -18

Combine like terms: 18 + -18 = 0
0 + x2 = 18.017769007 + -18
x2 = 18.017769007 + -18

Combine like terms: 18.017769007 + -18 = 0.017769007
x2 = 0.017769007

Simplifying
x2 = 0.017769007

Take the square root of each side:
x = {-0.133300439, 0.133300439}


Subproblem 2
x2 + 18 = -18.017769007

Simplifying
x2 + 18 = -18.017769007

Reorder the terms:
18 + x2 = -18.017769007

Solving
18 + x2 = -18.017769007

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x2 = -18.017769007 + -18

Combine like terms: 18 + -18 = 0
0 + x2 = -18.017769007 + -18
x2 = -18.017769007 + -18

Combine like terms: -18.017769007 + -18 = -36.017769007
x2 = -36.017769007

Simplifying
x2 = -36.017769007

Reorder the terms:
36.017769007 + x2 = -36.017769007 + 36.017769007

Combine like terms: -36.017769007 + 36.017769007 = 0.000000000
36.017769007 + 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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