d^4-238d^2-2866=0

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Solution for d^4-238d^2-2866=0 equation: 


Simplifying
d4 + -238d2 + -2866 = 0

Reorder the terms:
-2866 + -238d2 + d4 = 0

Solving
-2866 + -238d2 + d4 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '2866' to each side of the equation.
-2866 + -238d2 + 2866 + d4 = 0 + 2866

Reorder the terms:
-2866 + 2866 + -238d2 + d4 = 0 + 2866

Combine like terms: -2866 + 2866 = 0
0 + -238d2 + d4 = 0 + 2866
-238d2 + d4 = 0 + 2866

Combine like terms: 0 + 2866 = 2866
-238d2 + d4 = 2866

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 = 2866 + 14161

Reorder the terms:
14161 + -238d2 + d4 = 2866 + 14161

Combine like terms: 2866 + 14161 = 17027
14161 + -238d2 + d4 = 17027

Factor a perfect square on the left side:
(d2 + -119)(d2 + -119) = 17027

Calculate the square root of the right side: 130.487547299

Break this problem into two subproblems by setting 
(d2 + -119) equal to 130.487547299 and -130.487547299.


Subproblem 1
d2 + -119 = 130.487547299

Simplifying
d2 + -119 = 130.487547299

Reorder the terms:
-119 + d2 = 130.487547299

Solving
-119 + d2 = 130.487547299

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 = 130.487547299 + 119

Combine like terms: -119 + 119 = 0
0 + d2 = 130.487547299 + 119
d2 = 130.487547299 + 119

Combine like terms: 130.487547299 + 119 = 249.487547299
d2 = 249.487547299

Simplifying
d2 = 249.487547299

Take the square root of each side:
d = {-15.795174811, 15.795174811}


Subproblem 2
d2 + -119 = -130.487547299

Simplifying
d2 + -119 = -130.487547299

Reorder the terms:
-119 + d2 = -130.487547299

Solving
-119 + d2 = -130.487547299

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 = -130.487547299 + 119

Combine like terms: -119 + 119 = 0
0 + d2 = -130.487547299 + 119
d2 = -130.487547299 + 119

Combine like terms: -130.487547299 + 119 = -11.487547299
d2 = -11.487547299

Simplifying
d2 = -11.487547299

Reorder the terms:
11.487547299 + d2 = -11.487547299 + 11.487547299

Combine like terms: -11.487547299 + 11.487547299 = 0.000000000
11.487547299 + 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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