2p^2+20p-14=0

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Solution for 2p^2+20p-14=0 equation: 


Simplifying
2p2 + 20p + -14 = 0

Reorder the terms:
-14 + 20p + 2p2 = 0

Solving
-14 + 20p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 10p + p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 10p + p2)' equal to zero and attempt to solve:

Simplifying
-7 + 10p + p2 = 0

Solving
-7 + 10p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 10p + 7 + p2 = 0 + 7

Reorder the terms:
-7 + 7 + 10p + p2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 10p + p2 = 0 + 7
10p + p2 = 0 + 7

Combine like terms: 0 + 7 = 7
10p + p2 = 7

The p term is 10p.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10p + 25 + p2 = 7 + 25

Reorder the terms:
25 + 10p + p2 = 7 + 25

Combine like terms: 7 + 25 = 32
25 + 10p + p2 = 32

Factor a perfect square on the left side:
(p + 5)(p + 5) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(p + 5) equal to 5.656854249 and -5.656854249.


Subproblem 1
p + 5 = 5.656854249

Simplifying
p + 5 = 5.656854249

Reorder the terms:
5 + p = 5.656854249

Solving
5 + p = 5.656854249

Solving for variable 'p'.

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

Add '-5' to each side of the equation.
5 + -5 + p = 5.656854249 + -5

Combine like terms: 5 + -5 = 0
0 + p = 5.656854249 + -5
p = 5.656854249 + -5

Combine like terms: 5.656854249 + -5 = 0.656854249
p = 0.656854249

Simplifying
p = 0.656854249


Subproblem 2
p + 5 = -5.656854249

Simplifying
p + 5 = -5.656854249

Reorder the terms:
5 + p = -5.656854249

Solving
5 + p = -5.656854249

Solving for variable 'p'.

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

Add '-5' to each side of the equation.
5 + -5 + p = -5.656854249 + -5

Combine like terms: 5 + -5 = 0
0 + p = -5.656854249 + -5
p = -5.656854249 + -5

Combine like terms: -5.656854249 + -5 = -10.656854249
p = -10.656854249

Simplifying
p = -10.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.656854249, -10.656854249}
Solution
p = {0.656854249, -10.656854249}

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