p^2+14p-34=0

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Solution for p^2+14p-34=0 equation: 


Simplifying
p2 + 14p + -34 = 0

Reorder the terms:
-34 + 14p + p2 = 0

Solving
-34 + 14p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 14p + 34 + p2 = 0 + 34

Reorder the terms:
-34 + 34 + 14p + p2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 14p + p2 = 0 + 34
14p + p2 = 0 + 34

Combine like terms: 0 + 34 = 34
14p + p2 = 34

The p term is 14p.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14p + 49 + p2 = 34 + 49

Reorder the terms:
49 + 14p + p2 = 34 + 49

Combine like terms: 34 + 49 = 83
49 + 14p + p2 = 83

Factor a perfect square on the left side:
(p + 7)(p + 7) = 83

Calculate the square root of the right side: 9.110433579

Break this problem into two subproblems by setting 
(p + 7) equal to 9.110433579 and -9.110433579.


Subproblem 1
p + 7 = 9.110433579

Simplifying
p + 7 = 9.110433579

Reorder the terms:
7 + p = 9.110433579

Solving
7 + p = 9.110433579

Solving for variable 'p'.

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

Add '-7' to each side of the equation.
7 + -7 + p = 9.110433579 + -7

Combine like terms: 7 + -7 = 0
0 + p = 9.110433579 + -7
p = 9.110433579 + -7

Combine like terms: 9.110433579 + -7 = 2.110433579
p = 2.110433579

Simplifying
p = 2.110433579


Subproblem 2
p + 7 = -9.110433579

Simplifying
p + 7 = -9.110433579

Reorder the terms:
7 + p = -9.110433579

Solving
7 + p = -9.110433579

Solving for variable 'p'.

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

Add '-7' to each side of the equation.
7 + -7 + p = -9.110433579 + -7

Combine like terms: 7 + -7 = 0
0 + p = -9.110433579 + -7
p = -9.110433579 + -7

Combine like terms: -9.110433579 + -7 = -16.110433579
p = -16.110433579

Simplifying
p = -16.110433579


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.110433579, -16.110433579}

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