5p^2+16p+7=0

Solution for 5p^2+16p+7=0 equation:

Simplifying
5p2 + 16p + 7 = 0

Reorder the terms:
7 + 16p + 5p2 = 0

Solving
7 + 16p + 5p2 = 0

Solving for variable 'p'.

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

Divide each side by '5'.
1.4 + 3.2p + p2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + 3.2p + -1.4 + p2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + 3.2p + p2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + 3.2p + p2 = 0 + -1.4
3.2p + p2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
3.2p + p2 = -1.4

The p term is 3.2p.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2p + 2.56 + p2 = -1.4 + 2.56

Reorder the terms:
2.56 + 3.2p + p2 = -1.4 + 2.56

Combine like terms: -1.4 + 2.56 = 1.16
2.56 + 3.2p + p2 = 1.16

Factor a perfect square on the left side:
(p + 1.6)(p + 1.6) = 1.16

Calculate the square root of the right side: 1.077032961

Break this problem into two subproblems by setting 
(p + 1.6) equal to 1.077032961 and -1.077032961.

Subproblem 1
p + 1.6 = 1.077032961

Simplifying
p + 1.6 = 1.077032961

Reorder the terms:
1.6 + p = 1.077032961

Solving
1.6 + p = 1.077032961

Solving for variable 'p'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + p = 1.077032961 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + p = 1.077032961 + -1.6
p = 1.077032961 + -1.6

Combine like terms: 1.077032961 + -1.6 = -0.522967039
p = -0.522967039

Simplifying
p = -0.522967039

Subproblem 2
p + 1.6 = -1.077032961

Simplifying
p + 1.6 = -1.077032961

Reorder the terms:
1.6 + p = -1.077032961

Solving
1.6 + p = -1.077032961

Solving for variable 'p'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + p = -1.077032961 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + p = -1.077032961 + -1.6
p = -1.077032961 + -1.6

Combine like terms: -1.077032961 + -1.6 = -2.677032961
p = -2.677032961

Simplifying
p = -2.677032961

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.522967039, -2.677032961}