d^4-238d^2-2628=0

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Solution for d^4-238d^2-2628=0 equation: 


Simplifying
d4 + -238d2 + -2628 = 0

Reorder the terms:
-2628 + -238d2 + d4 = 0

Solving
-2628 + -238d2 + d4 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '2628' to each side of the equation.
-2628 + -238d2 + 2628 + d4 = 0 + 2628

Reorder the terms:
-2628 + 2628 + -238d2 + d4 = 0 + 2628

Combine like terms: -2628 + 2628 = 0
0 + -238d2 + d4 = 0 + 2628
-238d2 + d4 = 0 + 2628

Combine like terms: 0 + 2628 = 2628
-238d2 + d4 = 2628

The d term is -238d2.  Take half its coefficient (-119).
Square it (14161) and add it to both sides.

Add '14161' to each side of the equation.
-238d2 + 14161 + d4 = 2628 + 14161

Reorder the terms:
14161 + -238d2 + d4 = 2628 + 14161

Combine like terms: 2628 + 14161 = 16789
14161 + -238d2 + d4 = 16789

Factor a perfect square on the left side:
(d2 + -119)(d2 + -119) = 16789

Calculate the square root of the right side: 129.572373599

Break this problem into two subproblems by setting 
(d2 + -119) equal to 129.572373599 and -129.572373599.


Subproblem 1
d2 + -119 = 129.572373599

Simplifying
d2 + -119 = 129.572373599

Reorder the terms:
-119 + d2 = 129.572373599

Solving
-119 + d2 = 129.572373599

Solving for variable 'd'.

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

Add '119' to each side of the equation.
-119 + 119 + d2 = 129.572373599 + 119

Combine like terms: -119 + 119 = 0
0 + d2 = 129.572373599 + 119
d2 = 129.572373599 + 119

Combine like terms: 129.572373599 + 119 = 248.572373599
d2 = 248.572373599

Simplifying
d2 = 248.572373599

Take the square root of each side:
d = {-15.766178154, 15.766178154}


Subproblem 2
d2 + -119 = -129.572373599

Simplifying
d2 + -119 = -129.572373599

Reorder the terms:
-119 + d2 = -129.572373599

Solving
-119 + d2 = -129.572373599

Solving for variable 'd'.

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

Add '119' to each side of the equation.
-119 + 119 + d2 = -129.572373599 + 119

Combine like terms: -119 + 119 = 0
0 + d2 = -129.572373599 + 119
d2 = -129.572373599 + 119

Combine like terms: -129.572373599 + 119 = -10.572373599
d2 = -10.572373599

Simplifying
d2 = -10.572373599

Reorder the terms:
10.572373599 + d2 = -10.572373599 + 10.572373599

Combine like terms: -10.572373599 + 10.572373599 = 0.000000000
10.572373599 + d2 = 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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