-5.4412p^2+35.9486p+1.1834=0

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Solution for -5.4412p^2+35.9486p+1.1834=0 equation: 


Simplifying
-5.4412p2 + 35.9486p + 1.1834 = 0

Reorder the terms:
1.1834 + 35.9486p + -5.4412p2 = 0

Solving
1.1834 + 35.9486p + -5.4412p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
-5.4412 the coefficient of the squared term: 

Divide each side by '-5.4412'.
-0.2174887892 + -6.60674116p + p2 = 0

Move the constant term to the right:

Add '0.2174887892' to each side of the equation.
-0.2174887892 + -6.60674116p + 0.2174887892 + p2 = 0 + 0.2174887892

Reorder the terms:
-0.2174887892 + 0.2174887892 + -6.60674116p + p2 = 0 + 0.2174887892

Combine like terms: -0.2174887892 + 0.2174887892 = 0.0000000000
0.0000000000 + -6.60674116p + p2 = 0 + 0.2174887892
-6.60674116p + p2 = 0 + 0.2174887892

Combine like terms: 0 + 0.2174887892 = 0.2174887892
-6.60674116p + p2 = 0.2174887892

The p term is -6.60674116p.  Take half its coefficient (-3.30337058).
Square it (10.91225719) and add it to both sides.

Add '10.91225719' to each side of the equation.
-6.60674116p + 10.91225719 + p2 = 0.2174887892 + 10.91225719

Reorder the terms:
10.91225719 + -6.60674116p + p2 = 0.2174887892 + 10.91225719

Combine like terms: 0.2174887892 + 10.91225719 = 11.1297459792
10.91225719 + -6.60674116p + p2 = 11.1297459792

Factor a perfect square on the left side:
(p + -3.30337058)(p + -3.30337058) = 11.1297459792

Calculate the square root of the right side: 3.336127393

Break this problem into two subproblems by setting 
(p + -3.30337058) equal to 3.336127393 and -3.336127393.


Subproblem 1
p + -3.30337058 = 3.336127393

Simplifying
p + -3.30337058 = 3.336127393

Reorder the terms:
-3.30337058 + p = 3.336127393

Solving
-3.30337058 + p = 3.336127393

Solving for variable 'p'.

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

Add '3.30337058' to each side of the equation.
-3.30337058 + 3.30337058 + p = 3.336127393 + 3.30337058

Combine like terms: -3.30337058 + 3.30337058 = 0.00000000
0.00000000 + p = 3.336127393 + 3.30337058
p = 3.336127393 + 3.30337058

Combine like terms: 3.336127393 + 3.30337058 = 6.639497973
p = 6.639497973

Simplifying
p = 6.639497973


Subproblem 2
p + -3.30337058 = -3.336127393

Simplifying
p + -3.30337058 = -3.336127393

Reorder the terms:
-3.30337058 + p = -3.336127393

Solving
-3.30337058 + p = -3.336127393

Solving for variable 'p'.

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

Add '3.30337058' to each side of the equation.
-3.30337058 + 3.30337058 + p = -3.336127393 + 3.30337058

Combine like terms: -3.30337058 + 3.30337058 = 0.00000000
0.00000000 + p = -3.336127393 + 3.30337058
p = -3.336127393 + 3.30337058

Combine like terms: -3.336127393 + 3.30337058 = -0.032756813
p = -0.032756813

Simplifying
p = -0.032756813


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {6.639497973, -0.032756813}

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