p^2-18p-47=0

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Solution for p^2-18p-47=0 equation: 


Simplifying
p2 + -18p + -47 = 0

Reorder the terms:
-47 + -18p + p2 = 0

Solving
-47 + -18p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -18p + 47 + p2 = 0 + 47

Reorder the terms:
-47 + 47 + -18p + p2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -18p + p2 = 0 + 47
-18p + p2 = 0 + 47

Combine like terms: 0 + 47 = 47
-18p + p2 = 47

The p term is -18p.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18p + 81 + p2 = 47 + 81

Reorder the terms:
81 + -18p + p2 = 47 + 81

Combine like terms: 47 + 81 = 128
81 + -18p + p2 = 128

Factor a perfect square on the left side:
(p + -9)(p + -9) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(p + -9) equal to 11.313708499 and -11.313708499.


Subproblem 1
p + -9 = 11.313708499

Simplifying
p + -9 = 11.313708499

Reorder the terms:
-9 + p = 11.313708499

Solving
-9 + p = 11.313708499

Solving for variable 'p'.

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

Add '9' to each side of the equation.
-9 + 9 + p = 11.313708499 + 9

Combine like terms: -9 + 9 = 0
0 + p = 11.313708499 + 9
p = 11.313708499 + 9

Combine like terms: 11.313708499 + 9 = 20.313708499
p = 20.313708499

Simplifying
p = 20.313708499


Subproblem 2
p + -9 = -11.313708499

Simplifying
p + -9 = -11.313708499

Reorder the terms:
-9 + p = -11.313708499

Solving
-9 + p = -11.313708499

Solving for variable 'p'.

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

Add '9' to each side of the equation.
-9 + 9 + p = -11.313708499 + 9

Combine like terms: -9 + 9 = 0
0 + p = -11.313708499 + 9
p = -11.313708499 + 9

Combine like terms: -11.313708499 + 9 = -2.313708499
p = -2.313708499

Simplifying
p = -2.313708499


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {20.313708499, -2.313708499}

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