18750=2p^2+400p

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Solution for 18750=2p^2+400p equation: 


Simplifying
18750 = 2p2 + 400p

Reorder the terms:
18750 = 400p + 2p2

Solving
18750 = 400p + 2p2

Solving for variable 'p'.

Reorder the terms:
18750 + -400p + -2p2 = 400p + -400p + 2p2 + -2p2

Combine like terms: 400p + -400p = 0
18750 + -400p + -2p2 = 0 + 2p2 + -2p2
18750 + -400p + -2p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
18750 + -400p + -2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9375 + -200p + -1p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9375 + -200p + -1p2)' equal to zero and attempt to solve:

Simplifying
9375 + -200p + -1p2 = 0

Solving
9375 + -200p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-9375 + 200p + p2 = 0

Move the constant term to the right:

Add '9375' to each side of the equation.
-9375 + 200p + 9375 + p2 = 0 + 9375

Reorder the terms:
-9375 + 9375 + 200p + p2 = 0 + 9375

Combine like terms: -9375 + 9375 = 0
0 + 200p + p2 = 0 + 9375
200p + p2 = 0 + 9375

Combine like terms: 0 + 9375 = 9375
200p + p2 = 9375

The p term is 200p.  Take half its coefficient (100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
200p + 10000 + p2 = 9375 + 10000

Reorder the terms:
10000 + 200p + p2 = 9375 + 10000

Combine like terms: 9375 + 10000 = 19375
10000 + 200p + p2 = 19375

Factor a perfect square on the left side:
(p + 100)(p + 100) = 19375

Calculate the square root of the right side: 139.194109071

Break this problem into two subproblems by setting 
(p + 100) equal to 139.194109071 and -139.194109071.


Subproblem 1
p + 100 = 139.194109071

Simplifying
p + 100 = 139.194109071

Reorder the terms:
100 + p = 139.194109071

Solving
100 + p = 139.194109071

Solving for variable 'p'.

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

Add '-100' to each side of the equation.
100 + -100 + p = 139.194109071 + -100

Combine like terms: 100 + -100 = 0
0 + p = 139.194109071 + -100
p = 139.194109071 + -100

Combine like terms: 139.194109071 + -100 = 39.194109071
p = 39.194109071

Simplifying
p = 39.194109071


Subproblem 2
p + 100 = -139.194109071

Simplifying
p + 100 = -139.194109071

Reorder the terms:
100 + p = -139.194109071

Solving
100 + p = -139.194109071

Solving for variable 'p'.

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

Add '-100' to each side of the equation.
100 + -100 + p = -139.194109071 + -100

Combine like terms: 100 + -100 = 0
0 + p = -139.194109071 + -100
p = -139.194109071 + -100

Combine like terms: -139.194109071 + -100 = -239.194109071
p = -239.194109071

Simplifying
p = -239.194109071


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {39.194109071, -239.194109071}
Solution
p = {39.194109071, -239.194109071}

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