p^2-8p-3=0

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Solution for p^2-8p-3=0 equation: 


Simplifying
p2 + -8p + -3 = 0

Reorder the terms:
-3 + -8p + p2 = 0

Solving
-3 + -8p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -8p + 3 + p2 = 0 + 3

Reorder the terms:
-3 + 3 + -8p + p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8p + p2 = 0 + 3
-8p + p2 = 0 + 3

Combine like terms: 0 + 3 = 3
-8p + p2 = 3

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 = 3 + 16

Reorder the terms:
16 + -8p + p2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + -8p + p2 = 19

Factor a perfect square on the left side:
(p + -4)(p + -4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(p + -4) equal to 4.358898944 and -4.358898944.


Subproblem 1
p + -4 = 4.358898944

Simplifying
p + -4 = 4.358898944

Reorder the terms:
-4 + p = 4.358898944

Solving
-4 + p = 4.358898944

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 = 4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + p = 4.358898944 + 4
p = 4.358898944 + 4

Combine like terms: 4.358898944 + 4 = 8.358898944
p = 8.358898944

Simplifying
p = 8.358898944


Subproblem 2
p + -4 = -4.358898944

Simplifying
p + -4 = -4.358898944

Reorder the terms:
-4 + p = -4.358898944

Solving
-4 + p = -4.358898944

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 = -4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + p = -4.358898944 + 4
p = -4.358898944 + 4

Combine like terms: -4.358898944 + 4 = -0.358898944
p = -0.358898944

Simplifying
p = -0.358898944


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {8.358898944, -0.358898944}

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