p^2-4p-18=0

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Solution for p^2-4p-18=0 equation:


Simplifying
p2 + -4p + -18 = 0

Reorder the terms:
-18 + -4p + p2 = 0

Solving
-18 + -4p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -4p + 18 + p2 = 0 + 18

Reorder the terms:
-18 + 18 + -4p + p2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -4p + p2 = 0 + 18
-4p + p2 = 0 + 18

Combine like terms: 0 + 18 = 18
-4p + p2 = 18

The p term is -4p.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4p + 4 + p2 = 18 + 4

Reorder the terms:
4 + -4p + p2 = 18 + 4

Combine like terms: 18 + 4 = 22
4 + -4p + p2 = 22

Factor a perfect square on the left side:
(p + -2)(p + -2) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(p + -2) equal to 4.69041576 and -4.69041576.


Subproblem 1
p + -2 = 4.69041576

Simplifying
p + -2 = 4.69041576

Reorder the terms:
-2 + p = 4.69041576

Solving
-2 + p = 4.69041576

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = 4.69041576 + 2

Combine like terms: -2 + 2 = 0
0 + p = 4.69041576 + 2
p = 4.69041576 + 2

Combine like terms: 4.69041576 + 2 = 6.69041576
p = 6.69041576

Simplifying
p = 6.69041576


Subproblem 2
p + -2 = -4.69041576

Simplifying
p + -2 = -4.69041576

Reorder the terms:
-2 + p = -4.69041576

Solving
-2 + p = -4.69041576

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = -4.69041576 + 2

Combine like terms: -2 + 2 = 0
0 + p = -4.69041576 + 2
p = -4.69041576 + 2

Combine like terms: -4.69041576 + 2 = -2.69041576
p = -2.69041576

Simplifying
p = -2.69041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {6.69041576, -2.69041576}

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