d^4+16d^2-48=0

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Solution for d^4+16d^2-48=0 equation: 


Simplifying
d4 + 16d2 + -48 = 0

Reorder the terms:
-48 + 16d2 + d4 = 0

Solving
-48 + 16d2 + d4 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 16d2 + 48 + d4 = 0 + 48

Reorder the terms:
-48 + 48 + 16d2 + d4 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 16d2 + d4 = 0 + 48
16d2 + d4 = 0 + 48

Combine like terms: 0 + 48 = 48
16d2 + d4 = 48

The d term is 16d2.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16d2 + 64 + d4 = 48 + 64

Reorder the terms:
64 + 16d2 + d4 = 48 + 64

Combine like terms: 48 + 64 = 112
64 + 16d2 + d4 = 112

Factor a perfect square on the left side:
(d2 + 8)(d2 + 8) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(d2 + 8) equal to 10.583005244 and -10.583005244.


Subproblem 1
d2 + 8 = 10.583005244

Simplifying
d2 + 8 = 10.583005244

Reorder the terms:
8 + d2 = 10.583005244

Solving
8 + d2 = 10.583005244

Solving for variable 'd'.

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

Add '-8' to each side of the equation.
8 + -8 + d2 = 10.583005244 + -8

Combine like terms: 8 + -8 = 0
0 + d2 = 10.583005244 + -8
d2 = 10.583005244 + -8

Combine like terms: 10.583005244 + -8 = 2.583005244
d2 = 2.583005244

Simplifying
d2 = 2.583005244

Take the square root of each side:
d = {-1.60717306, 1.60717306}


Subproblem 2
d2 + 8 = -10.583005244

Simplifying
d2 + 8 = -10.583005244

Reorder the terms:
8 + d2 = -10.583005244

Solving
8 + d2 = -10.583005244

Solving for variable 'd'.

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

Add '-8' to each side of the equation.
8 + -8 + d2 = -10.583005244 + -8

Combine like terms: 8 + -8 = 0
0 + d2 = -10.583005244 + -8
d2 = -10.583005244 + -8

Combine like terms: -10.583005244 + -8 = -18.583005244
d2 = -18.583005244

Simplifying
d2 = -18.583005244

Reorder the terms:
18.583005244 + d2 = -18.583005244 + 18.583005244

Combine like terms: -18.583005244 + 18.583005244 = 0.000000000
18.583005244 + 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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