4p^2+20p+7=0

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Solution for 4p^2+20p+7=0 equation: 


Simplifying
4p2 + 20p + 7 = 0

Reorder the terms:
7 + 20p + 4p2 = 0

Solving
7 + 20p + 4p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
1.75 + 5p + p2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 5p + -1.75 + p2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 5p + p2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 5p + p2 = 0 + -1.75
5p + p2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
5p + p2 = -1.75

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 = -1.75 + 6.25

Reorder the terms:
6.25 + 5p + p2 = -1.75 + 6.25

Combine like terms: -1.75 + 6.25 = 4.5
6.25 + 5p + p2 = 4.5

Factor a perfect square on the left side:
(p + 2.5)(p + 2.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(p + 2.5) equal to 2.121320344 and -2.121320344.


Subproblem 1
p + 2.5 = 2.121320344

Simplifying
p + 2.5 = 2.121320344

Reorder the terms:
2.5 + p = 2.121320344

Solving
2.5 + p = 2.121320344

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 = 2.121320344 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = 2.121320344 + -2.5
p = 2.121320344 + -2.5

Combine like terms: 2.121320344 + -2.5 = -0.378679656
p = -0.378679656

Simplifying
p = -0.378679656


Subproblem 2
p + 2.5 = -2.121320344

Simplifying
p + 2.5 = -2.121320344

Reorder the terms:
2.5 + p = -2.121320344

Solving
2.5 + p = -2.121320344

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 = -2.121320344 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = -2.121320344 + -2.5
p = -2.121320344 + -2.5

Combine like terms: -2.121320344 + -2.5 = -4.621320344
p = -4.621320344

Simplifying
p = -4.621320344


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.378679656, -4.621320344}

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