0=p^2+5p+2

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Solution for 0=p^2+5p+2 equation: 


Simplifying
0 = p2 + 5p + 2

Reorder the terms:
0 = 2 + 5p + p2

Solving
0 = 2 + 5p + p2

Solving for variable 'p'.

Combine like terms: 0 + -2 = -2
-2 + -5p + -1p2 = 2 + 5p + p2 + -2 + -5p + -1p2

Reorder the terms:
-2 + -5p + -1p2 = 2 + -2 + 5p + -5p + p2 + -1p2

Combine like terms: 2 + -2 = 0
-2 + -5p + -1p2 = 0 + 5p + -5p + p2 + -1p2
-2 + -5p + -1p2 = 5p + -5p + p2 + -1p2

Combine like terms: 5p + -5p = 0
-2 + -5p + -1p2 = 0 + p2 + -1p2
-2 + -5p + -1p2 = p2 + -1p2

Combine like terms: p2 + -1p2 = 0
-2 + -5p + -1p2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 5p + p2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 5p + p2)' equal to zero and attempt to solve:

Simplifying
2 + 5p + p2 = 0

Solving
2 + 5p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5p + -2 + p2 = 0 + -2

Reorder the terms:
2 + -2 + 5p + p2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5p + p2 = 0 + -2
5p + p2 = 0 + -2

Combine like terms: 0 + -2 = -2
5p + p2 = -2

The p term is 5p.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5p + 6.25 + p2 = -2 + 6.25

Reorder the terms:
6.25 + 5p + p2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + 5p + p2 = 4.25

Factor a perfect square on the left side:
(p + 2.5)(p + 2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(p + 2.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
p + 2.5 = 2.061552813

Simplifying
p + 2.5 = 2.061552813

Reorder the terms:
2.5 + p = 2.061552813

Solving
2.5 + p = 2.061552813

Solving for variable 'p'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + p = 2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = 2.061552813 + -2.5
p = 2.061552813 + -2.5

Combine like terms: 2.061552813 + -2.5 = -0.438447187
p = -0.438447187

Simplifying
p = -0.438447187


Subproblem 2
p + 2.5 = -2.061552813

Simplifying
p + 2.5 = -2.061552813

Reorder the terms:
2.5 + p = -2.061552813

Solving
2.5 + p = -2.061552813

Solving for variable 'p'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + p = -2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = -2.061552813 + -2.5
p = -2.061552813 + -2.5

Combine like terms: -2.061552813 + -2.5 = -4.561552813
p = -4.561552813

Simplifying
p = -4.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.438447187, -4.561552813}
Solution
p = {-0.438447187, -4.561552813}

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