x^4-35x^2+21.7=0

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Solution for x^4-35x^2+21.7=0 equation: 


Simplifying
x4 + -35x2 + 21.7 = 0

Reorder the terms:
21.7 + -35x2 + x4 = 0

Solving
21.7 + -35x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-21.7' to each side of the equation.
21.7 + -35x2 + -21.7 + x4 = 0 + -21.7

Reorder the terms:
21.7 + -21.7 + -35x2 + x4 = 0 + -21.7

Combine like terms: 21.7 + -21.7 = 0.0
0.0 + -35x2 + x4 = 0 + -21.7
-35x2 + x4 = 0 + -21.7

Combine like terms: 0 + -21.7 = -21.7
-35x2 + x4 = -21.7

The x term is -35x2.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x2 + 306.25 + x4 = -21.7 + 306.25

Reorder the terms:
306.25 + -35x2 + x4 = -21.7 + 306.25

Combine like terms: -21.7 + 306.25 = 284.55
306.25 + -35x2 + x4 = 284.55

Factor a perfect square on the left side:
(x2 + -17.5)(x2 + -17.5) = 284.55

Calculate the square root of the right side: 16.868609901

Break this problem into two subproblems by setting 
(x2 + -17.5) equal to 16.868609901 and -16.868609901.


Subproblem 1
x2 + -17.5 = 16.868609901

Simplifying
x2 + -17.5 = 16.868609901

Reorder the terms:
-17.5 + x2 = 16.868609901

Solving
-17.5 + x2 = 16.868609901

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x2 = 16.868609901 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x2 = 16.868609901 + 17.5
x2 = 16.868609901 + 17.5

Combine like terms: 16.868609901 + 17.5 = 34.368609901
x2 = 34.368609901

Simplifying
x2 = 34.368609901

Take the square root of each side:
x = {-5.862474725, 5.862474725}


Subproblem 2
x2 + -17.5 = -16.868609901

Simplifying
x2 + -17.5 = -16.868609901

Reorder the terms:
-17.5 + x2 = -16.868609901

Solving
-17.5 + x2 = -16.868609901

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x2 = -16.868609901 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x2 = -16.868609901 + 17.5
x2 = -16.868609901 + 17.5

Combine like terms: -16.868609901 + 17.5 = 0.631390099
x2 = 0.631390099

Simplifying
x2 = 0.631390099

Take the square root of each side:
x = {-0.794600591, 0.794600591}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.862474725, 5.862474725, -0.794600591, 0.794600591}

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