p^2-4p-64=0

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Solution for p^2-4p-64=0 equation: 


Simplifying
p2 + -4p + -64 = 0

Reorder the terms:
-64 + -4p + p2 = 0

Solving
-64 + -4p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -4p + 64 + p2 = 0 + 64

Reorder the terms:
-64 + 64 + -4p + p2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -4p + p2 = 0 + 64
-4p + p2 = 0 + 64

Combine like terms: 0 + 64 = 64
-4p + p2 = 64

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 = 64 + 4

Reorder the terms:
4 + -4p + p2 = 64 + 4

Combine like terms: 64 + 4 = 68
4 + -4p + p2 = 68

Factor a perfect square on the left side:
(p + -2)(p + -2) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(p + -2) equal to 8.246211251 and -8.246211251.


Subproblem 1
p + -2 = 8.246211251

Simplifying
p + -2 = 8.246211251

Reorder the terms:
-2 + p = 8.246211251

Solving
-2 + p = 8.246211251

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 = 8.246211251 + 2

Combine like terms: -2 + 2 = 0
0 + p = 8.246211251 + 2
p = 8.246211251 + 2

Combine like terms: 8.246211251 + 2 = 10.246211251
p = 10.246211251

Simplifying
p = 10.246211251


Subproblem 2
p + -2 = -8.246211251

Simplifying
p + -2 = -8.246211251

Reorder the terms:
-2 + p = -8.246211251

Solving
-2 + p = -8.246211251

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 = -8.246211251 + 2

Combine like terms: -2 + 2 = 0
0 + p = -8.246211251 + 2
p = -8.246211251 + 2

Combine like terms: -8.246211251 + 2 = -6.246211251
p = -6.246211251

Simplifying
p = -6.246211251


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {10.246211251, -6.246211251}

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