20x^4-18x^2-11=0

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Solution for 20x^4-18x^2-11=0 equation: 


Simplifying
20x4 + -18x2 + -11 = 0

Reorder the terms:
-11 + -18x2 + 20x4 = 0

Solving
-11 + -18x2 + 20x4 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-0.55 + -0.9x2 + x4 = 0

Move the constant term to the right:

Add '0.55' to each side of the equation.
-0.55 + -0.9x2 + 0.55 + x4 = 0 + 0.55

Reorder the terms:
-0.55 + 0.55 + -0.9x2 + x4 = 0 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + -0.9x2 + x4 = 0 + 0.55
-0.9x2 + x4 = 0 + 0.55

Combine like terms: 0 + 0.55 = 0.55
-0.9x2 + x4 = 0.55

The x term is -0.9x2.  Take half its coefficient (-0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
-0.9x2 + 0.2025 + x4 = 0.55 + 0.2025

Reorder the terms:
0.2025 + -0.9x2 + x4 = 0.55 + 0.2025

Combine like terms: 0.55 + 0.2025 = 0.7525
0.2025 + -0.9x2 + x4 = 0.7525

Factor a perfect square on the left side:
(x2 + -0.45)(x2 + -0.45) = 0.7525

Calculate the square root of the right side: 0.867467579

Break this problem into two subproblems by setting 
(x2 + -0.45) equal to 0.867467579 and -0.867467579.


Subproblem 1
x2 + -0.45 = 0.867467579

Simplifying
x2 + -0.45 = 0.867467579

Reorder the terms:
-0.45 + x2 = 0.867467579

Solving
-0.45 + x2 = 0.867467579

Solving for variable 'x'.

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

Add '0.45' to each side of the equation.
-0.45 + 0.45 + x2 = 0.867467579 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + x2 = 0.867467579 + 0.45
x2 = 0.867467579 + 0.45

Combine like terms: 0.867467579 + 0.45 = 1.317467579
x2 = 1.317467579

Simplifying
x2 = 1.317467579

Take the square root of each side:
x = {-1.147809905, 1.147809905}


Subproblem 2
x2 + -0.45 = -0.867467579

Simplifying
x2 + -0.45 = -0.867467579

Reorder the terms:
-0.45 + x2 = -0.867467579

Solving
-0.45 + x2 = -0.867467579

Solving for variable 'x'.

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

Add '0.45' to each side of the equation.
-0.45 + 0.45 + x2 = -0.867467579 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + x2 = -0.867467579 + 0.45
x2 = -0.867467579 + 0.45

Combine like terms: -0.867467579 + 0.45 = -0.417467579
x2 = -0.417467579

Simplifying
x2 = -0.417467579

Reorder the terms:
0.417467579 + x2 = -0.417467579 + 0.417467579

Combine like terms: -0.417467579 + 0.417467579 = 0.000000000
0.417467579 + 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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