2x^4-40x^2+50=0

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Solution for 2x^4-40x^2+50=0 equation: 


Simplifying
2x4 + -40x2 + 50 = 0

Reorder the terms:
50 + -40x2 + 2x4 = 0

Solving
50 + -40x2 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -20x2 + x4) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + -20x2 + x4)' equal to zero and attempt to solve:

Simplifying
25 + -20x2 + x4 = 0

Solving
25 + -20x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -20x2 + -25 + x4 = 0 + -25

Reorder the terms:
25 + -25 + -20x2 + x4 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -20x2 + x4 = 0 + -25
-20x2 + x4 = 0 + -25

Combine like terms: 0 + -25 = -25
-20x2 + x4 = -25

The x term is -20x2.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x2 + 100 + x4 = -25 + 100

Reorder the terms:
100 + -20x2 + x4 = -25 + 100

Combine like terms: -25 + 100 = 75
100 + -20x2 + x4 = 75

Factor a perfect square on the left side:
(x2 + -10)(x2 + -10) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x2 + -10) equal to 8.660254038 and -8.660254038.


Subproblem 1
x2 + -10 = 8.660254038

Simplifying
x2 + -10 = 8.660254038

Reorder the terms:
-10 + x2 = 8.660254038

Solving
-10 + x2 = 8.660254038

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x2 = 8.660254038 + 10

Combine like terms: -10 + 10 = 0
0 + x2 = 8.660254038 + 10
x2 = 8.660254038 + 10

Combine like terms: 8.660254038 + 10 = 18.660254038
x2 = 18.660254038

Simplifying
x2 = 18.660254038

Take the square root of each side:
x = {-4.319751618, 4.319751618}


Subproblem 2
x2 + -10 = -8.660254038

Simplifying
x2 + -10 = -8.660254038

Reorder the terms:
-10 + x2 = -8.660254038

Solving
-10 + x2 = -8.660254038

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x2 = -8.660254038 + 10

Combine like terms: -10 + 10 = 0
0 + x2 = -8.660254038 + 10
x2 = -8.660254038 + 10

Combine like terms: -8.660254038 + 10 = 1.339745962
x2 = 1.339745962

Simplifying
x2 = 1.339745962

Take the square root of each side:
x = {-1.157473957, 1.157473957}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.319751618, 4.319751618, -1.157473957, 1.157473957}
Solution
x = {-4.319751618, 4.319751618, -1.157473957, 1.157473957}

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