-5p^2+15000p-1750000=0

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Solution for -5p^2+15000p-1750000=0 equation: 


Simplifying
-5p2 + 15000p + -1750000 = 0

Reorder the terms:
-1750000 + 15000p + -5p2 = 0

Solving
-1750000 + 15000p + -5p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-350000 + 3000p + -1p2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-350000 + 3000p + -1p2)' equal to zero and attempt to solve:

Simplifying
-350000 + 3000p + -1p2 = 0

Solving
-350000 + 3000p + -1p2 = 0

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

Divide each side by '-1'.
350000 + -3000p + p2 = 0

Move the constant term to the right:

Add '-350000' to each side of the equation.
350000 + -3000p + -350000 + p2 = 0 + -350000

Reorder the terms:
350000 + -350000 + -3000p + p2 = 0 + -350000

Combine like terms: 350000 + -350000 = 0
0 + -3000p + p2 = 0 + -350000
-3000p + p2 = 0 + -350000

Combine like terms: 0 + -350000 = -350000
-3000p + p2 = -350000

The p term is -3000p.  Take half its coefficient (-1500).
Square it (2250000) and add it to both sides.

Add '2250000' to each side of the equation.
-3000p + 2250000 + p2 = -350000 + 2250000

Reorder the terms:
2250000 + -3000p + p2 = -350000 + 2250000

Combine like terms: -350000 + 2250000 = 1900000
2250000 + -3000p + p2 = 1900000

Factor a perfect square on the left side:
(p + -1500)(p + -1500) = 1900000

Calculate the square root of the right side: 1378.404875209

Break this problem into two subproblems by setting 
(p + -1500) equal to 1378.404875209 and -1378.404875209.


Subproblem 1
p + -1500 = 1378.404875209

Simplifying
p + -1500 = 1378.404875209

Reorder the terms:
-1500 + p = 1378.404875209

Solving
-1500 + p = 1378.404875209

Solving for variable 'p'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + p = 1378.404875209 + 1500

Combine like terms: -1500 + 1500 = 0
0 + p = 1378.404875209 + 1500
p = 1378.404875209 + 1500

Combine like terms: 1378.404875209 + 1500 = 2878.404875209
p = 2878.404875209

Simplifying
p = 2878.404875209


Subproblem 2
p + -1500 = -1378.404875209

Simplifying
p + -1500 = -1378.404875209

Reorder the terms:
-1500 + p = -1378.404875209

Solving
-1500 + p = -1378.404875209

Solving for variable 'p'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + p = -1378.404875209 + 1500

Combine like terms: -1500 + 1500 = 0
0 + p = -1378.404875209 + 1500
p = -1378.404875209 + 1500

Combine like terms: -1378.404875209 + 1500 = 121.595124791
p = 121.595124791

Simplifying
p = 121.595124791


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2878.404875209, 121.595124791}
Solution
p = {2878.404875209, 121.595124791}

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