2p^6+p^3-10000=0

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Solution for 2p^6+p^3-10000=0 equation: 


Simplifying
2p6 + p3 + -10000 = 0

Reorder the terms:
-10000 + p3 + 2p6 = 0

Solving
-10000 + p3 + 2p6 = 0

Solving for variable 'p'.

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

Divide each side by '2'.
-5000 + 0.5p3 + p6 = 0

Move the constant term to the right:

Add '5000' to each side of the equation.
-5000 + 0.5p3 + 5000 + p6 = 0 + 5000

Reorder the terms:
-5000 + 5000 + 0.5p3 + p6 = 0 + 5000

Combine like terms: -5000 + 5000 = 0
0 + 0.5p3 + p6 = 0 + 5000
0.5p3 + p6 = 0 + 5000

Combine like terms: 0 + 5000 = 5000
0.5p3 + p6 = 5000

The p term is p3.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5p3 + 0.25 + p6 = 5000 + 0.25

Reorder the terms:
0.25 + 0.5p3 + p6 = 5000 + 0.25

Combine like terms: 5000 + 0.25 = 5000.25
0.25 + 0.5p3 + p6 = 5000.25

Factor a perfect square on the left side:
(p3 + 0.5)(p3 + 0.5) = 5000.25

Calculate the square root of the right side: 70.712445864

Break this problem into two subproblems by setting 
(p3 + 0.5) equal to 70.712445864 and -70.712445864.


Subproblem 1
p3 + 0.5 = 70.712445864

Simplifying
p3 + 0.5 = 70.712445864

Reorder the terms:
0.5 + p3 = 70.712445864

Solving
0.5 + p3 = 70.712445864

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p3 = 70.712445864 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p3 = 70.712445864 + -0.5
p3 = 70.712445864 + -0.5

Combine like terms: 70.712445864 + -0.5 = 70.212445864
p3 = 70.212445864

Simplifying
p3 = 70.212445864

Reorder the terms:
-70.212445864 + p3 = 70.212445864 + -70.212445864

Combine like terms: 70.212445864 + -70.212445864 = 0.000000000
-70.212445864 + p3 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
p3 + 0.5 = -70.712445864

Simplifying
p3 + 0.5 = -70.712445864

Reorder the terms:
0.5 + p3 = -70.712445864

Solving
0.5 + p3 = -70.712445864

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p3 = -70.712445864 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p3 = -70.712445864 + -0.5
p3 = -70.712445864 + -0.5

Combine like terms: -70.712445864 + -0.5 = -71.212445864
p3 = -71.212445864

Simplifying
p3 = -71.212445864

Reorder the terms:
71.212445864 + p3 = -71.212445864 + 71.212445864

Combine like terms: -71.212445864 + 71.212445864 = 0.000000000
71.212445864 + p3 = 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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