x^4+40x^2+20=0

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Solution for x^4+40x^2+20=0 equation:


Simplifying
x4 + 40x2 + 20 = 0

Reorder the terms:
20 + 40x2 + x4 = 0

Solving
20 + 40x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 40x2 + -20 + x4 = 0 + -20

Reorder the terms:
20 + -20 + 40x2 + x4 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 40x2 + x4 = 0 + -20
40x2 + x4 = 0 + -20

Combine like terms: 0 + -20 = -20
40x2 + x4 = -20

The x term is 40x2.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x2 + 400 + x4 = -20 + 400

Reorder the terms:
400 + 40x2 + x4 = -20 + 400

Combine like terms: -20 + 400 = 380
400 + 40x2 + x4 = 380

Factor a perfect square on the left side:
(x2 + 20)(x2 + 20) = 380

Calculate the square root of the right side: 19.49358869

Break this problem into two subproblems by setting 
(x2 + 20) equal to 19.49358869 and -19.49358869.

Subproblem 1

x2 + 20 = 19.49358869 Simplifying x2 + 20 = 19.49358869 Reorder the terms: 20 + x2 = 19.49358869 Solving 20 + x2 = 19.49358869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x2 = 19.49358869 + -20 Combine like terms: 20 + -20 = 0 0 + x2 = 19.49358869 + -20 x2 = 19.49358869 + -20 Combine like terms: 19.49358869 + -20 = -0.50641131 x2 = -0.50641131 Simplifying x2 = -0.50641131 Reorder the terms: 0.50641131 + x2 = -0.50641131 + 0.50641131 Combine like terms: -0.50641131 + 0.50641131 = 0.00000000 0.50641131 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2

x2 + 20 = -19.49358869 Simplifying x2 + 20 = -19.49358869 Reorder the terms: 20 + x2 = -19.49358869 Solving 20 + x2 = -19.49358869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x2 = -19.49358869 + -20 Combine like terms: 20 + -20 = 0 0 + x2 = -19.49358869 + -20 x2 = -19.49358869 + -20 Combine like terms: -19.49358869 + -20 = -39.49358869 x2 = -39.49358869 Simplifying x2 = -39.49358869 Reorder the terms: 39.49358869 + x2 = -39.49358869 + 39.49358869 Combine like terms: -39.49358869 + 39.49358869 = 0.00000000 39.49358869 + 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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