1.44p^2+6p+6.25=0

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Solution for 1.44p^2+6p+6.25=0 equation: 


Simplifying
1.44p2 + 6p + 6.25 = 0

Reorder the terms:
6.25 + 6p + 1.44p2 = 0

Solving
6.25 + 6p + 1.44p2 = 0

Solving for variable 'p'.

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

Divide each side by '1.44'.
4.340277778 + 4.166666667p + p2 = 0

Move the constant term to the right:

Add '-4.340277778' to each side of the equation.
4.340277778 + 4.166666667p + -4.340277778 + p2 = 0 + -4.340277778

Reorder the terms:
4.340277778 + -4.340277778 + 4.166666667p + p2 = 0 + -4.340277778

Combine like terms: 4.340277778 + -4.340277778 = 0.000000000
0.000000000 + 4.166666667p + p2 = 0 + -4.340277778
4.166666667p + p2 = 0 + -4.340277778

Combine like terms: 0 + -4.340277778 = -4.340277778
4.166666667p + p2 = -4.340277778

The p term is 4.166666667p.  Take half its coefficient (2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
4.166666667p + 4.340277781 + p2 = -4.340277778 + 4.340277781

Reorder the terms:
4.340277781 + 4.166666667p + p2 = -4.340277778 + 4.340277781

Combine like terms: -4.340277778 + 4.340277781 = 0.000000003
4.340277781 + 4.166666667p + p2 = 0.000000003

Factor a perfect square on the left side:
(p + 2.083333334)(p + 2.083333334) = 0.000000003

Calculate the square root of the right side: 0.000054772

Break this problem into two subproblems by setting 
(p + 2.083333334) equal to 0.000054772 and -0.000054772.


Subproblem 1
p + 2.083333334 = 0.000054772

Simplifying
p + 2.083333334 = 0.000054772

Reorder the terms:
2.083333334 + p = 0.000054772

Solving
2.083333334 + p = 0.000054772

Solving for variable 'p'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + p = 0.000054772 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + p = 0.000054772 + -2.083333334
p = 0.000054772 + -2.083333334

Combine like terms: 0.000054772 + -2.083333334 = -2.083278562
p = -2.083278562

Simplifying
p = -2.083278562


Subproblem 2
p + 2.083333334 = -0.000054772

Simplifying
p + 2.083333334 = -0.000054772

Reorder the terms:
2.083333334 + p = -0.000054772

Solving
2.083333334 + p = -0.000054772

Solving for variable 'p'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + p = -0.000054772 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + p = -0.000054772 + -2.083333334
p = -0.000054772 + -2.083333334

Combine like terms: -0.000054772 + -2.083333334 = -2.083388106
p = -2.083388106

Simplifying
p = -2.083388106


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-2.083278562, -2.083388106}

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