(s+4)(s+4)=s+80

Solution for (s+4)(s+4)=s+80 equation:

Simplifying
(s + 4)(s + 4) = s + 80

Reorder the terms:
(4 + s)(s + 4) = s + 80

Reorder the terms:
(4 + s)(4 + s) = s + 80

Multiply (4 + s) * (4 + s)
(4(4 + s) + s(4 + s)) = s + 80
((4 * 4 + s * 4) + s(4 + s)) = s + 80
((16 + 4s) + s(4 + s)) = s + 80
(16 + 4s + (4 * s + s * s)) = s + 80
(16 + 4s + (4s + s2)) = s + 80

Combine like terms: 4s + 4s = 8s
(16 + 8s + s2) = s + 80

Reorder the terms:
16 + 8s + s2 = 80 + s

Solving
16 + 8s + s2 = 80 + s

Solving for variable 's'.

Reorder the terms:
16 + -80 + 8s + -1s + s2 = 80 + s + -80 + -1s

Combine like terms: 16 + -80 = -64
-64 + 8s + -1s + s2 = 80 + s + -80 + -1s

Combine like terms: 8s + -1s = 7s
-64 + 7s + s2 = 80 + s + -80 + -1s

Reorder the terms:
-64 + 7s + s2 = 80 + -80 + s + -1s

Combine like terms: 80 + -80 = 0
-64 + 7s + s2 = 0 + s + -1s
-64 + 7s + s2 = s + -1s

Combine like terms: s + -1s = 0
-64 + 7s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 7s + 64 + s2 = 0 + 64

Reorder the terms:
-64 + 64 + 7s + s2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 7s + s2 = 0 + 64
7s + s2 = 0 + 64

Combine like terms: 0 + 64 = 64
7s + s2 = 64

The s term is 7s.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7s + 12.25 + s2 = 64 + 12.25

Reorder the terms:
12.25 + 7s + s2 = 64 + 12.25

Combine like terms: 64 + 12.25 = 76.25
12.25 + 7s + s2 = 76.25

Factor a perfect square on the left side:
(s + 3.5)(s + 3.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(s + 3.5) equal to 8.732124598 and -8.732124598.

Subproblem 1
s + 3.5 = 8.732124598

Simplifying
s + 3.5 = 8.732124598

Reorder the terms:
3.5 + s = 8.732124598

Solving
3.5 + s = 8.732124598

Solving for variable 's'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + s = 8.732124598 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + s = 8.732124598 + -3.5
s = 8.732124598 + -3.5

Combine like terms: 8.732124598 + -3.5 = 5.232124598
s = 5.232124598

Simplifying
s = 5.232124598

Subproblem 2
s + 3.5 = -8.732124598

Simplifying
s + 3.5 = -8.732124598

Reorder the terms:
3.5 + s = -8.732124598

Solving
3.5 + s = -8.732124598

Solving for variable 's'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + s = -8.732124598 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + s = -8.732124598 + -3.5
s = -8.732124598 + -3.5

Combine like terms: -8.732124598 + -3.5 = -12.232124598
s = -12.232124598

Simplifying
s = -12.232124598

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {5.232124598, -12.232124598}