-P^2+11P=5

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Solution for -P^2+11P=5 equation:


Simplifying
-1P2 + 11P = 5

Reorder the terms:
11P + -1P2 = 5

Solving
11P + -1P2 = 5

Solving for variable 'P'.

Reorder the terms:
-5 + 11P + -1P2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 11P + -1P2 = 0

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

Divide each side by '-1'.
5 + -11P + P2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -11P + -5 + P2 = 0 + -5

Reorder the terms:
5 + -5 + -11P + P2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -11P + P2 = 0 + -5
-11P + P2 = 0 + -5

Combine like terms: 0 + -5 = -5
-11P + P2 = -5

The P term is -11P.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11P + 30.25 + P2 = -5 + 30.25

Reorder the terms:
30.25 + -11P + P2 = -5 + 30.25

Combine like terms: -5 + 30.25 = 25.25
30.25 + -11P + P2 = 25.25

Factor a perfect square on the left side:
(P + -5.5)(P + -5.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(P + -5.5) equal to 5.024937811 and -5.024937811.

Subproblem 1

P + -5.5 = 5.024937811 Simplifying P + -5.5 = 5.024937811 Reorder the terms: -5.5 + P = 5.024937811 Solving -5.5 + P = 5.024937811 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + P = 5.024937811 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + P = 5.024937811 + 5.5 P = 5.024937811 + 5.5 Combine like terms: 5.024937811 + 5.5 = 10.524937811 P = 10.524937811 Simplifying P = 10.524937811

Subproblem 2

P + -5.5 = -5.024937811 Simplifying P + -5.5 = -5.024937811 Reorder the terms: -5.5 + P = -5.024937811 Solving -5.5 + P = -5.024937811 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + P = -5.024937811 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + P = -5.024937811 + 5.5 P = -5.024937811 + 5.5 Combine like terms: -5.024937811 + 5.5 = 0.475062189 P = 0.475062189 Simplifying P = 0.475062189

Solution

The solution to the problem is based on the solutions from the subproblems. P = {10.524937811, 0.475062189}

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