4x^4+25x^2-160=0

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Solution for 4x^4+25x^2-160=0 equation: 


Simplifying
4x4 + 25x2 + -160 = 0

Reorder the terms:
-160 + 25x2 + 4x4 = 0

Solving
-160 + 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'.
-40 + 6.25x2 + x4 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 6.25x2 + 40 + x4 = 0 + 40

Reorder the terms:
-40 + 40 + 6.25x2 + x4 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 6.25x2 + x4 = 0 + 40
6.25x2 + x4 = 0 + 40

Combine like terms: 0 + 40 = 40
6.25x2 + x4 = 40

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 = 40 + 9.765625

Reorder the terms:
9.765625 + 6.25x2 + x4 = 40 + 9.765625

Combine like terms: 40 + 9.765625 = 49.765625
9.765625 + 6.25x2 + x4 = 49.765625

Factor a perfect square on the left side:
(x2 + 3.125)(x2 + 3.125) = 49.765625

Calculate the square root of the right side: 7.05447553

Break this problem into two subproblems by setting 
(x2 + 3.125) equal to 7.05447553 and -7.05447553.


Subproblem 1
x2 + 3.125 = 7.05447553

Simplifying
x2 + 3.125 = 7.05447553

Reorder the terms:
3.125 + x2 = 7.05447553

Solving
3.125 + x2 = 7.05447553

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 = 7.05447553 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x2 = 7.05447553 + -3.125
x2 = 7.05447553 + -3.125

Combine like terms: 7.05447553 + -3.125 = 3.92947553
x2 = 3.92947553

Simplifying
x2 = 3.92947553

Take the square root of each side:
x = {-1.982290476, 1.982290476}


Subproblem 2
x2 + 3.125 = -7.05447553

Simplifying
x2 + 3.125 = -7.05447553

Reorder the terms:
3.125 + x2 = -7.05447553

Solving
3.125 + x2 = -7.05447553

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 = -7.05447553 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x2 = -7.05447553 + -3.125
x2 = -7.05447553 + -3.125

Combine like terms: -7.05447553 + -3.125 = -10.17947553
x2 = -10.17947553

Simplifying
x2 = -10.17947553

Reorder the terms:
10.17947553 + x2 = -10.17947553 + 10.17947553

Combine like terms: -10.17947553 + 10.17947553 = 0.00000000
10.17947553 + 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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