-2p^2+4000p-500000=0

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Solution for -2p^2+4000p-500000=0 equation: 


Simplifying
-2p2 + 4000p + -500000 = 0

Reorder the terms:
-500000 + 4000p + -2p2 = 0

Solving
-500000 + 4000p + -2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-250000 + 2000p + -1p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-250000 + 2000p + -1p2)' equal to zero and attempt to solve:

Simplifying
-250000 + 2000p + -1p2 = 0

Solving
-250000 + 2000p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
250000 + -2000p + p2 = 0

Move the constant term to the right:

Add '-250000' to each side of the equation.
250000 + -2000p + -250000 + p2 = 0 + -250000

Reorder the terms:
250000 + -250000 + -2000p + p2 = 0 + -250000

Combine like terms: 250000 + -250000 = 0
0 + -2000p + p2 = 0 + -250000
-2000p + p2 = 0 + -250000

Combine like terms: 0 + -250000 = -250000
-2000p + p2 = -250000

The p term is -2000p.  Take half its coefficient (-1000).
Square it (1000000) and add it to both sides.

Add '1000000' to each side of the equation.
-2000p + 1000000 + p2 = -250000 + 1000000

Reorder the terms:
1000000 + -2000p + p2 = -250000 + 1000000

Combine like terms: -250000 + 1000000 = 750000
1000000 + -2000p + p2 = 750000

Factor a perfect square on the left side:
(p + -1000)(p + -1000) = 750000

Calculate the square root of the right side: 866.025403784

Break this problem into two subproblems by setting 
(p + -1000) equal to 866.025403784 and -866.025403784.


Subproblem 1
p + -1000 = 866.025403784

Simplifying
p + -1000 = 866.025403784

Reorder the terms:
-1000 + p = 866.025403784

Solving
-1000 + p = 866.025403784

Solving for variable 'p'.

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

Add '1000' to each side of the equation.
-1000 + 1000 + p = 866.025403784 + 1000

Combine like terms: -1000 + 1000 = 0
0 + p = 866.025403784 + 1000
p = 866.025403784 + 1000

Combine like terms: 866.025403784 + 1000 = 1866.025403784
p = 1866.025403784

Simplifying
p = 1866.025403784


Subproblem 2
p + -1000 = -866.025403784

Simplifying
p + -1000 = -866.025403784

Reorder the terms:
-1000 + p = -866.025403784

Solving
-1000 + p = -866.025403784

Solving for variable 'p'.

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

Add '1000' to each side of the equation.
-1000 + 1000 + p = -866.025403784 + 1000

Combine like terms: -1000 + 1000 = 0
0 + p = -866.025403784 + 1000
p = -866.025403784 + 1000

Combine like terms: -866.025403784 + 1000 = 133.974596216
p = 133.974596216

Simplifying
p = 133.974596216


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1866.025403784, 133.974596216}
Solution
p = {1866.025403784, 133.974596216}

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