-x^4+100x^2+50=0

Solution for -x^4+100x^2+50=0 equation:

Simplifying
-1x4 + 100x2 + 50 = 0

Reorder the terms:
50 + 100x2 + -1x4 = 0

Solving
50 + 100x2 + -1x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-50 + -100x2 + x4 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -100x2 + 50 + x4 = 0 + 50

Reorder the terms:
-50 + 50 + -100x2 + x4 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -100x2 + x4 = 0 + 50
-100x2 + x4 = 0 + 50

Combine like terms: 0 + 50 = 50
-100x2 + x4 = 50

The x term is -100x2.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x2 + 2500 + x4 = 50 + 2500

Reorder the terms:
2500 + -100x2 + x4 = 50 + 2500

Combine like terms: 50 + 2500 = 2550
2500 + -100x2 + x4 = 2550

Factor a perfect square on the left side:
(x2 + -50)(x2 + -50) = 2550

Calculate the square root of the right side: 50.497524692

Break this problem into two subproblems by setting 
(x2 + -50) equal to 50.497524692 and -50.497524692.

Subproblem 1
x2 + -50 = 50.497524692

Simplifying
x2 + -50 = 50.497524692

Reorder the terms:
-50 + x2 = 50.497524692

Solving
-50 + x2 = 50.497524692

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x2 = 50.497524692 + 50

Combine like terms: -50 + 50 = 0
0 + x2 = 50.497524692 + 50
x2 = 50.497524692 + 50

Combine like terms: 50.497524692 + 50 = 100.497524692
x2 = 100.497524692

Simplifying
x2 = 100.497524692

Take the square root of each side:
x = {-10.02484537, 10.02484537}

Subproblem 2
x2 + -50 = -50.497524692

Simplifying
x2 + -50 = -50.497524692

Reorder the terms:
-50 + x2 = -50.497524692

Solving
-50 + x2 = -50.497524692

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x2 = -50.497524692 + 50

Combine like terms: -50 + 50 = 0
0 + x2 = -50.497524692 + 50
x2 = -50.497524692 + 50

Combine like terms: -50.497524692 + 50 = -0.497524692
x2 = -0.497524692

Simplifying
x2 = -0.497524692

Reorder the terms:
0.497524692 + x2 = -0.497524692 + 0.497524692

Combine like terms: -0.497524692 + 0.497524692 = 0.000000000
0.497524692 + 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.