2p^2+20p+46=0

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Solution for 2p^2+20p+46=0 equation: 


Simplifying
2p2 + 20p + 46 = 0

Reorder the terms:
46 + 20p + 2p2 = 0

Solving
46 + 20p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(23 + 10p + p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(23 + 10p + p2)' equal to zero and attempt to solve:

Simplifying
23 + 10p + p2 = 0

Solving
23 + 10p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 10p + -23 + p2 = 0 + -23

Reorder the terms:
23 + -23 + 10p + p2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 10p + p2 = 0 + -23
10p + p2 = 0 + -23

Combine like terms: 0 + -23 = -23
10p + p2 = -23

The p term is 10p.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10p + 25 + p2 = -23 + 25

Reorder the terms:
25 + 10p + p2 = -23 + 25

Combine like terms: -23 + 25 = 2
25 + 10p + p2 = 2

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

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(p + 5) equal to 1.414213562 and -1.414213562.


Subproblem 1
p + 5 = 1.414213562

Simplifying
p + 5 = 1.414213562

Reorder the terms:
5 + p = 1.414213562

Solving
5 + p = 1.414213562

Solving for variable 'p'.

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

Add '-5' to each side of the equation.
5 + -5 + p = 1.414213562 + -5

Combine like terms: 5 + -5 = 0
0 + p = 1.414213562 + -5
p = 1.414213562 + -5

Combine like terms: 1.414213562 + -5 = -3.585786438
p = -3.585786438

Simplifying
p = -3.585786438


Subproblem 2
p + 5 = -1.414213562

Simplifying
p + 5 = -1.414213562

Reorder the terms:
5 + p = -1.414213562

Solving
5 + p = -1.414213562

Solving for variable 'p'.

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

Add '-5' to each side of the equation.
5 + -5 + p = -1.414213562 + -5

Combine like terms: 5 + -5 = 0
0 + p = -1.414213562 + -5
p = -1.414213562 + -5

Combine like terms: -1.414213562 + -5 = -6.414213562
p = -6.414213562

Simplifying
p = -6.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-3.585786438, -6.414213562}
Solution
p = {-3.585786438, -6.414213562}

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