3p^2+11p=2

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Solution for 3p^2+11p=2 equation: 


Simplifying
3p2 + 11p = 2

Reorder the terms:
11p + 3p2 = 2

Solving
11p + 3p2 = 2

Solving for variable 'p'.

Reorder the terms:
-2 + 11p + 3p2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 11p + 3p2 = 0

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

Divide each side by '3'.
-0.6666666667 + 3.666666667p + p2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 3.666666667p + 0.6666666667 + p2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 3.666666667p + p2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 3.666666667p + p2 = 0 + 0.6666666667
3.666666667p + p2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
3.666666667p + p2 = 0.6666666667

The p term is 3.666666667p.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667p + 3.361111114 + p2 = 0.6666666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667p + p2 = 0.6666666667 + 3.361111114

Combine like terms: 0.6666666667 + 3.361111114 = 4.0277777807
3.361111114 + 3.666666667p + p2 = 4.0277777807

Factor a perfect square on the left side:
(p + 1.833333334)(p + 1.833333334) = 4.0277777807

Calculate the square root of the right side: 2.006932431

Break this problem into two subproblems by setting 
(p + 1.833333334) equal to 2.006932431 and -2.006932431.


Subproblem 1
p + 1.833333334 = 2.006932431

Simplifying
p + 1.833333334 = 2.006932431

Reorder the terms:
1.833333334 + p = 2.006932431

Solving
1.833333334 + p = 2.006932431

Solving for variable 'p'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + p = 2.006932431 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + p = 2.006932431 + -1.833333334
p = 2.006932431 + -1.833333334

Combine like terms: 2.006932431 + -1.833333334 = 0.173599097
p = 0.173599097

Simplifying
p = 0.173599097


Subproblem 2
p + 1.833333334 = -2.006932431

Simplifying
p + 1.833333334 = -2.006932431

Reorder the terms:
1.833333334 + p = -2.006932431

Solving
1.833333334 + p = -2.006932431

Solving for variable 'p'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + p = -2.006932431 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + p = -2.006932431 + -1.833333334
p = -2.006932431 + -1.833333334

Combine like terms: -2.006932431 + -1.833333334 = -3.840265765
p = -3.840265765

Simplifying
p = -3.840265765


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.173599097, -3.840265765}

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