0.7p^2-28p-1014.3=0

Solution for 0.7p^2-28p-1014.3=0 equation:

Simplifying
0.7p2 + -28p + -1014.3 = 0

Reorder the terms:
-1014.3 + -28p + 0.7p2 = 0

Solving
-1014.3 + -28p + 0.7p2 = 0

Solving for variable 'p'.

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

Divide each side by '0.7'.
-1449 + -40p + p2 = 0

Move the constant term to the right:

Add '1449' to each side of the equation.
-1449 + -40p + 1449 + p2 = 0 + 1449

Reorder the terms:
-1449 + 1449 + -40p + p2 = 0 + 1449

Combine like terms: -1449 + 1449 = 0
0 + -40p + p2 = 0 + 1449
-40p + p2 = 0 + 1449

Combine like terms: 0 + 1449 = 1449
-40p + p2 = 1449

The p term is -40p.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40p + 400 + p2 = 1449 + 400

Reorder the terms:
400 + -40p + p2 = 1449 + 400

Combine like terms: 1449 + 400 = 1849
400 + -40p + p2 = 1849

Factor a perfect square on the left side:
(p + -20)(p + -20) = 1849

Calculate the square root of the right side: 43

Break this problem into two subproblems by setting 
(p + -20) equal to 43 and -43.

Subproblem 1
p + -20 = 43

Simplifying
p + -20 = 43

Reorder the terms:
-20 + p = 43

Solving
-20 + p = 43

Solving for variable 'p'.

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

Add '20' to each side of the equation.
-20 + 20 + p = 43 + 20

Combine like terms: -20 + 20 = 0
0 + p = 43 + 20
p = 43 + 20

Combine like terms: 43 + 20 = 63
p = 63

Simplifying
p = 63

Subproblem 2
p + -20 = -43

Simplifying
p + -20 = -43

Reorder the terms:
-20 + p = -43

Solving
-20 + p = -43

Solving for variable 'p'.

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

Add '20' to each side of the equation.
-20 + 20 + p = -43 + 20

Combine like terms: -20 + 20 = 0
0 + p = -43 + 20
p = -43 + 20

Combine like terms: -43 + 20 = -23
p = -23

Simplifying
p = -23

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {63, -23}