p^2-8p-74=0

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Solution for p^2-8p-74=0 equation: 


Simplifying
p2 + -8p + -74 = 0

Reorder the terms:
-74 + -8p + p2 = 0

Solving
-74 + -8p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + -8p + 74 + p2 = 0 + 74

Reorder the terms:
-74 + 74 + -8p + p2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + -8p + p2 = 0 + 74
-8p + p2 = 0 + 74

Combine like terms: 0 + 74 = 74
-8p + p2 = 74

The p term is -8p.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8p + 16 + p2 = 74 + 16

Reorder the terms:
16 + -8p + p2 = 74 + 16

Combine like terms: 74 + 16 = 90
16 + -8p + p2 = 90

Factor a perfect square on the left side:
(p + -4)(p + -4) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(p + -4) equal to 9.486832981 and -9.486832981.


Subproblem 1
p + -4 = 9.486832981

Simplifying
p + -4 = 9.486832981

Reorder the terms:
-4 + p = 9.486832981

Solving
-4 + p = 9.486832981

Solving for variable 'p'.

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

Add '4' to each side of the equation.
-4 + 4 + p = 9.486832981 + 4

Combine like terms: -4 + 4 = 0
0 + p = 9.486832981 + 4
p = 9.486832981 + 4

Combine like terms: 9.486832981 + 4 = 13.486832981
p = 13.486832981

Simplifying
p = 13.486832981


Subproblem 2
p + -4 = -9.486832981

Simplifying
p + -4 = -9.486832981

Reorder the terms:
-4 + p = -9.486832981

Solving
-4 + p = -9.486832981

Solving for variable 'p'.

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

Add '4' to each side of the equation.
-4 + 4 + p = -9.486832981 + 4

Combine like terms: -4 + 4 = 0
0 + p = -9.486832981 + 4
p = -9.486832981 + 4

Combine like terms: -9.486832981 + 4 = -5.486832981
p = -5.486832981

Simplifying
p = -5.486832981


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {13.486832981, -5.486832981}

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