x^4-21x^2-80=0

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Solution for x^4-21x^2-80=0 equation: 


Simplifying
x4 + -21x2 + -80 = 0

Reorder the terms:
-80 + -21x2 + x4 = 0

Solving
-80 + -21x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -21x2 + 80 + x4 = 0 + 80

Reorder the terms:
-80 + 80 + -21x2 + x4 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -21x2 + x4 = 0 + 80
-21x2 + x4 = 0 + 80

Combine like terms: 0 + 80 = 80
-21x2 + x4 = 80

The x term is -21x2.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x2 + 110.25 + x4 = 80 + 110.25

Reorder the terms:
110.25 + -21x2 + x4 = 80 + 110.25

Combine like terms: 80 + 110.25 = 190.25
110.25 + -21x2 + x4 = 190.25

Factor a perfect square on the left side:
(x2 + -10.5)(x2 + -10.5) = 190.25

Calculate the square root of the right side: 13.793114224

Break this problem into two subproblems by setting 
(x2 + -10.5) equal to 13.793114224 and -13.793114224.


Subproblem 1
x2 + -10.5 = 13.793114224

Simplifying
x2 + -10.5 = 13.793114224

Reorder the terms:
-10.5 + x2 = 13.793114224

Solving
-10.5 + x2 = 13.793114224

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x2 = 13.793114224 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x2 = 13.793114224 + 10.5
x2 = 13.793114224 + 10.5

Combine like terms: 13.793114224 + 10.5 = 24.293114224
x2 = 24.293114224

Simplifying
x2 = 24.293114224

Take the square root of each side:
x = {-4.928804543, 4.928804543}


Subproblem 2
x2 + -10.5 = -13.793114224

Simplifying
x2 + -10.5 = -13.793114224

Reorder the terms:
-10.5 + x2 = -13.793114224

Solving
-10.5 + x2 = -13.793114224

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x2 = -13.793114224 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x2 = -13.793114224 + 10.5
x2 = -13.793114224 + 10.5

Combine like terms: -13.793114224 + 10.5 = -3.293114224
x2 = -3.293114224

Simplifying
x2 = -3.293114224

Reorder the terms:
3.293114224 + x2 = -3.293114224 + 3.293114224

Combine like terms: -3.293114224 + 3.293114224 = 0.000000000
3.293114224 + 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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