-200P^2+3000P-1300=0

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Solution for -200P^2+3000P-1300=0 equation: 


Simplifying
-200P2 + 3000P + -1300 = 0

Reorder the terms:
-1300 + 3000P + -200P2 = 0

Solving
-1300 + 3000P + -200P2 = 0

Solving for variable 'P'.

Factor out the Greatest Common Factor (GCF), '100'.
100(-13 + 30P + -2P2) = 0

Ignore the factor 100.

Subproblem 1
Set the factor '(-13 + 30P + -2P2)' equal to zero and attempt to solve:

Simplifying
-13 + 30P + -2P2 = 0

Solving
-13 + 30P + -2P2 = 0

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

Divide each side by '-2'.
6.5 + -15P + P2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -15P + -6.5 + P2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -15P + P2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -15P + P2 = 0 + -6.5
-15P + P2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-15P + P2 = -6.5

The P term is -15P.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15P + 56.25 + P2 = -6.5 + 56.25

Reorder the terms:
56.25 + -15P + P2 = -6.5 + 56.25

Combine like terms: -6.5 + 56.25 = 49.75
56.25 + -15P + P2 = 49.75

Factor a perfect square on the left side:
(P + -7.5)(P + -7.5) = 49.75

Calculate the square root of the right side: 7.05336799

Break this problem into two subproblems by setting 
(P + -7.5) equal to 7.05336799 and -7.05336799.


Subproblem 1
P + -7.5 = 7.05336799

Simplifying
P + -7.5 = 7.05336799

Reorder the terms:
-7.5 + P = 7.05336799

Solving
-7.5 + P = 7.05336799

Solving for variable 'P'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + P = 7.05336799 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + P = 7.05336799 + 7.5
P = 7.05336799 + 7.5

Combine like terms: 7.05336799 + 7.5 = 14.55336799
P = 14.55336799

Simplifying
P = 14.55336799


Subproblem 2
P + -7.5 = -7.05336799

Simplifying
P + -7.5 = -7.05336799

Reorder the terms:
-7.5 + P = -7.05336799

Solving
-7.5 + P = -7.05336799

Solving for variable 'P'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + P = -7.05336799 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + P = -7.05336799 + 7.5
P = -7.05336799 + 7.5

Combine like terms: -7.05336799 + 7.5 = 0.44663201
P = 0.44663201

Simplifying
P = 0.44663201


Solution
The solution to the problem is based on the solutions
from the subproblems.
P = {14.55336799, 0.44663201}
Solution
P = {14.55336799, 0.44663201}

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