2p^2+112p-390=0

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Solution for 2p^2+112p-390=0 equation: 


Simplifying
2p2 + 112p + -390 = 0

Reorder the terms:
-390 + 112p + 2p2 = 0

Solving
-390 + 112p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-195 + 56p + p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-195 + 56p + p2)' equal to zero and attempt to solve:

Simplifying
-195 + 56p + p2 = 0

Solving
-195 + 56p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '195' to each side of the equation.
-195 + 56p + 195 + p2 = 0 + 195

Reorder the terms:
-195 + 195 + 56p + p2 = 0 + 195

Combine like terms: -195 + 195 = 0
0 + 56p + p2 = 0 + 195
56p + p2 = 0 + 195

Combine like terms: 0 + 195 = 195
56p + p2 = 195

The p term is 56p.  Take half its coefficient (28).
Square it (784) and add it to both sides.

Add '784' to each side of the equation.
56p + 784 + p2 = 195 + 784

Reorder the terms:
784 + 56p + p2 = 195 + 784

Combine like terms: 195 + 784 = 979
784 + 56p + p2 = 979

Factor a perfect square on the left side:
(p + 28)(p + 28) = 979

Calculate the square root of the right side: 31.288975694

Break this problem into two subproblems by setting 
(p + 28) equal to 31.288975694 and -31.288975694.


Subproblem 1
p + 28 = 31.288975694

Simplifying
p + 28 = 31.288975694

Reorder the terms:
28 + p = 31.288975694

Solving
28 + p = 31.288975694

Solving for variable 'p'.

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

Add '-28' to each side of the equation.
28 + -28 + p = 31.288975694 + -28

Combine like terms: 28 + -28 = 0
0 + p = 31.288975694 + -28
p = 31.288975694 + -28

Combine like terms: 31.288975694 + -28 = 3.288975694
p = 3.288975694

Simplifying
p = 3.288975694


Subproblem 2
p + 28 = -31.288975694

Simplifying
p + 28 = -31.288975694

Reorder the terms:
28 + p = -31.288975694

Solving
28 + p = -31.288975694

Solving for variable 'p'.

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

Add '-28' to each side of the equation.
28 + -28 + p = -31.288975694 + -28

Combine like terms: 28 + -28 = 0
0 + p = -31.288975694 + -28
p = -31.288975694 + -28

Combine like terms: -31.288975694 + -28 = -59.288975694
p = -59.288975694

Simplifying
p = -59.288975694


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.288975694, -59.288975694}
Solution
p = {3.288975694, -59.288975694}

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