x^4-29x^2=100

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Solution for x^4-29x^2=100 equation: 


Simplifying
x4 + -29x2 = 100

Reorder the terms:
-29x2 + x4 = 100

Solving
-29x2 + x4 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + -29x2 + x4 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -29x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -29x2 + 100 + x4 = 0 + 100

Reorder the terms:
-100 + 100 + -29x2 + x4 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -29x2 + x4 = 0 + 100
-29x2 + x4 = 0 + 100

Combine like terms: 0 + 100 = 100
-29x2 + x4 = 100

The x term is -29x2.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29x2 + 210.25 + x4 = 100 + 210.25

Reorder the terms:
210.25 + -29x2 + x4 = 100 + 210.25

Combine like terms: 100 + 210.25 = 310.25
210.25 + -29x2 + x4 = 310.25

Factor a perfect square on the left side:
(x2 + -14.5)(x2 + -14.5) = 310.25

Calculate the square root of the right side: 17.613914954

Break this problem into two subproblems by setting 
(x2 + -14.5) equal to 17.613914954 and -17.613914954.


Subproblem 1
x2 + -14.5 = 17.613914954

Simplifying
x2 + -14.5 = 17.613914954

Reorder the terms:
-14.5 + x2 = 17.613914954

Solving
-14.5 + x2 = 17.613914954

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x2 = 17.613914954 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x2 = 17.613914954 + 14.5
x2 = 17.613914954 + 14.5

Combine like terms: 17.613914954 + 14.5 = 32.113914954
x2 = 32.113914954

Simplifying
x2 = 32.113914954

Take the square root of each side:
x = {-5.666914059, 5.666914059}


Subproblem 2
x2 + -14.5 = -17.613914954

Simplifying
x2 + -14.5 = -17.613914954

Reorder the terms:
-14.5 + x2 = -17.613914954

Solving
-14.5 + x2 = -17.613914954

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x2 = -17.613914954 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x2 = -17.613914954 + 14.5
x2 = -17.613914954 + 14.5

Combine like terms: -17.613914954 + 14.5 = -3.113914954
x2 = -3.113914954

Simplifying
x2 = -3.113914954

Reorder the terms:
3.113914954 + x2 = -3.113914954 + 3.113914954

Combine like terms: -3.113914954 + 3.113914954 = 0.000000000
3.113914954 + 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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