p^2+4p=1

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Solution for p^2+4p=1 equation: 


Simplifying
p2 + 4p = 1

Reorder the terms:
4p + p2 = 1

Solving
4p + p2 = 1

Solving for variable 'p'.

Reorder the terms:
-1 + 4p + p2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 4p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + 4p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4p + p2 = 0 + 1
4p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
4p + p2 = 1

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 = 1 + 4

Reorder the terms:
4 + 4p + p2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + 4p + p2 = 5

Factor a perfect square on the left side:
(p + 2)(p + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(p + 2) equal to 2.236067978 and -2.236067978.


Subproblem 1
p + 2 = 2.236067978

Simplifying
p + 2 = 2.236067978

Reorder the terms:
2 + p = 2.236067978

Solving
2 + p = 2.236067978

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 = 2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + p = 2.236067978 + -2
p = 2.236067978 + -2

Combine like terms: 2.236067978 + -2 = 0.236067978
p = 0.236067978

Simplifying
p = 0.236067978


Subproblem 2
p + 2 = -2.236067978

Simplifying
p + 2 = -2.236067978

Reorder the terms:
2 + p = -2.236067978

Solving
2 + p = -2.236067978

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 = -2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + p = -2.236067978 + -2
p = -2.236067978 + -2

Combine like terms: -2.236067978 + -2 = -4.236067978
p = -4.236067978

Simplifying
p = -4.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.236067978, -4.236067978}

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