4x^4-25x^2-36=0

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Solution for 4x^4-25x^2-36=0 equation: 


Simplifying
4x4 + -25x2 + -36 = 0

Reorder the terms:
-36 + -25x2 + 4x4 = 0

Solving
-36 + -25x2 + 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'.
-9 + -6.25x2 + x4 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -6.25x2 + 9 + x4 = 0 + 9

Reorder the terms:
-9 + 9 + -6.25x2 + x4 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -6.25x2 + x4 = 0 + 9
-6.25x2 + x4 = 0 + 9

Combine like terms: 0 + 9 = 9
-6.25x2 + x4 = 9

The x term is -6.25x2.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x2 + 9.765625 + x4 = 9 + 9.765625

Reorder the terms:
9.765625 + -6.25x2 + x4 = 9 + 9.765625

Combine like terms: 9 + 9.765625 = 18.765625
9.765625 + -6.25x2 + x4 = 18.765625

Factor a perfect square on the left side:
(x2 + -3.125)(x2 + -3.125) = 18.765625

Calculate the square root of the right side: 4.331930863

Break this problem into two subproblems by setting 
(x2 + -3.125) equal to 4.331930863 and -4.331930863.


Subproblem 1
x2 + -3.125 = 4.331930863

Simplifying
x2 + -3.125 = 4.331930863

Reorder the terms:
-3.125 + x2 = 4.331930863

Solving
-3.125 + x2 = 4.331930863

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x2 = 4.331930863 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x2 = 4.331930863 + 3.125
x2 = 4.331930863 + 3.125

Combine like terms: 4.331930863 + 3.125 = 7.456930863
x2 = 7.456930863

Simplifying
x2 = 7.456930863

Take the square root of each side:
x = {-2.730738154, 2.730738154}


Subproblem 2
x2 + -3.125 = -4.331930863

Simplifying
x2 + -3.125 = -4.331930863

Reorder the terms:
-3.125 + x2 = -4.331930863

Solving
-3.125 + x2 = -4.331930863

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x2 = -4.331930863 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x2 = -4.331930863 + 3.125
x2 = -4.331930863 + 3.125

Combine like terms: -4.331930863 + 3.125 = -1.206930863
x2 = -1.206930863

Simplifying
x2 = -1.206930863

Reorder the terms:
1.206930863 + x2 = -1.206930863 + 1.206930863

Combine like terms: -1.206930863 + 1.206930863 = 0.000000000
1.206930863 + 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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