2p^2-15p-28=0

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Solution for 2p^2-15p-28=0 equation: 


Simplifying
2p2 + -15p + -28 = 0

Reorder the terms:
-28 + -15p + 2p2 = 0

Solving
-28 + -15p + 2p2 = 0

Solving for variable 'p'.

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

Divide each side by '2'.
-14 + -7.5p + p2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -7.5p + 14 + p2 = 0 + 14

Reorder the terms:
-14 + 14 + -7.5p + p2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -7.5p + p2 = 0 + 14
-7.5p + p2 = 0 + 14

Combine like terms: 0 + 14 = 14
-7.5p + p2 = 14

The p term is -7.5p.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5p + 14.0625 + p2 = 14 + 14.0625

Reorder the terms:
14.0625 + -7.5p + p2 = 14 + 14.0625

Combine like terms: 14 + 14.0625 = 28.0625
14.0625 + -7.5p + p2 = 28.0625

Factor a perfect square on the left side:
(p + -3.75)(p + -3.75) = 28.0625

Calculate the square root of the right side: 5.297405025

Break this problem into two subproblems by setting 
(p + -3.75) equal to 5.297405025 and -5.297405025.


Subproblem 1
p + -3.75 = 5.297405025

Simplifying
p + -3.75 = 5.297405025

Reorder the terms:
-3.75 + p = 5.297405025

Solving
-3.75 + p = 5.297405025

Solving for variable 'p'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + p = 5.297405025 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + p = 5.297405025 + 3.75
p = 5.297405025 + 3.75

Combine like terms: 5.297405025 + 3.75 = 9.047405025
p = 9.047405025

Simplifying
p = 9.047405025


Subproblem 2
p + -3.75 = -5.297405025

Simplifying
p + -3.75 = -5.297405025

Reorder the terms:
-3.75 + p = -5.297405025

Solving
-3.75 + p = -5.297405025

Solving for variable 'p'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + p = -5.297405025 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + p = -5.297405025 + 3.75
p = -5.297405025 + 3.75

Combine like terms: -5.297405025 + 3.75 = -1.547405025
p = -1.547405025

Simplifying
p = -1.547405025


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {9.047405025, -1.547405025}

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