p^2+14p-29=0

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Solution for p^2+14p-29=0 equation: 


Simplifying
p2 + 14p + -29 = 0

Reorder the terms:
-29 + 14p + p2 = 0

Solving
-29 + 14p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 14p + 29 + p2 = 0 + 29

Reorder the terms:
-29 + 29 + 14p + p2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 14p + p2 = 0 + 29
14p + p2 = 0 + 29

Combine like terms: 0 + 29 = 29
14p + p2 = 29

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 = 29 + 49

Reorder the terms:
49 + 14p + p2 = 29 + 49

Combine like terms: 29 + 49 = 78
49 + 14p + p2 = 78

Factor a perfect square on the left side:
(p + 7)(p + 7) = 78

Calculate the square root of the right side: 8.831760866

Break this problem into two subproblems by setting 
(p + 7) equal to 8.831760866 and -8.831760866.


Subproblem 1
p + 7 = 8.831760866

Simplifying
p + 7 = 8.831760866

Reorder the terms:
7 + p = 8.831760866

Solving
7 + p = 8.831760866

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 = 8.831760866 + -7

Combine like terms: 7 + -7 = 0
0 + p = 8.831760866 + -7
p = 8.831760866 + -7

Combine like terms: 8.831760866 + -7 = 1.831760866
p = 1.831760866

Simplifying
p = 1.831760866


Subproblem 2
p + 7 = -8.831760866

Simplifying
p + 7 = -8.831760866

Reorder the terms:
7 + p = -8.831760866

Solving
7 + p = -8.831760866

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 = -8.831760866 + -7

Combine like terms: 7 + -7 = 0
0 + p = -8.831760866 + -7
p = -8.831760866 + -7

Combine like terms: -8.831760866 + -7 = -15.831760866
p = -15.831760866

Simplifying
p = -15.831760866


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.831760866, -15.831760866}

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