(10p^2)-40000p-4008000000=0

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Solution for (10p^2)-40000p-4008000000=0 equation: 


Simplifying
(10p2) + -40000p + -4008000000 = 0

Reorder the terms:
-4008000000 + -40000p + (10p2) = 0

Solving
-4008000000 + -40000p + (10p2) = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-400800000 + -4000p + p2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-400800000 + -4000p + p2)' equal to zero and attempt to solve:

Simplifying
-400800000 + -4000p + p2 = 0

Solving
-400800000 + -4000p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '400800000' to each side of the equation.
-400800000 + -4000p + 400800000 + p2 = 0 + 400800000

Reorder the terms:
-400800000 + 400800000 + -4000p + p2 = 0 + 400800000

Combine like terms: -400800000 + 400800000 = 0
0 + -4000p + p2 = 0 + 400800000
-4000p + p2 = 0 + 400800000

Combine like terms: 0 + 400800000 = 400800000
-4000p + p2 = 400800000

The p term is -4000p.  Take half its coefficient (-2000).
Square it (4000000) and add it to both sides.

Add '4000000' to each side of the equation.
-4000p + 4000000 + p2 = 400800000 + 4000000

Reorder the terms:
4000000 + -4000p + p2 = 400800000 + 4000000

Combine like terms: 400800000 + 4000000 = 404800000
4000000 + -4000p + p2 = 404800000

Factor a perfect square on the left side:
(p + -2000)(p + -2000) = 404800000

Calculate the square root of the right side: 20119.642143935

Break this problem into two subproblems by setting 
(p + -2000) equal to 20119.642143935 and -20119.642143935.


Subproblem 1
p + -2000 = 20119.642143935

Simplifying
p + -2000 = 20119.642143935

Reorder the terms:
-2000 + p = 20119.642143935

Solving
-2000 + p = 20119.642143935

Solving for variable 'p'.

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

Add '2000' to each side of the equation.
-2000 + 2000 + p = 20119.642143935 + 2000

Combine like terms: -2000 + 2000 = 0
0 + p = 20119.642143935 + 2000
p = 20119.642143935 + 2000

Combine like terms: 20119.642143935 + 2000 = 22119.642143935
p = 22119.642143935

Simplifying
p = 22119.642143935


Subproblem 2
p + -2000 = -20119.642143935

Simplifying
p + -2000 = -20119.642143935

Reorder the terms:
-2000 + p = -20119.642143935

Solving
-2000 + p = -20119.642143935

Solving for variable 'p'.

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

Add '2000' to each side of the equation.
-2000 + 2000 + p = -20119.642143935 + 2000

Combine like terms: -2000 + 2000 = 0
0 + p = -20119.642143935 + 2000
p = -20119.642143935 + 2000

Combine like terms: -20119.642143935 + 2000 = -18119.642143935
p = -18119.642143935

Simplifying
p = -18119.642143935


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {22119.642143935, -18119.642143935}
Solution
p = {22119.642143935, -18119.642143935}

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