2s^2+8s-52=0

Solution for 2s^2+8s-52=0 equation:

Simplifying
2s2 + 8s + -52 = 0

Reorder the terms:
-52 + 8s + 2s2 = 0

Solving
-52 + 8s + 2s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-26 + 4s + s2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-26 + 4s + s2)' equal to zero and attempt to solve:

Simplifying
-26 + 4s + s2 = 0

Solving
-26 + 4s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 4s + 26 + s2 = 0 + 26

Reorder the terms:
-26 + 26 + 4s + s2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 4s + s2 = 0 + 26
4s + s2 = 0 + 26

Combine like terms: 0 + 26 = 26
4s + s2 = 26

The s term is 4s.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4s + 4 + s2 = 26 + 4

Reorder the terms:
4 + 4s + s2 = 26 + 4

Combine like terms: 26 + 4 = 30
4 + 4s + s2 = 30

Factor a perfect square on the left side:
(s + 2)(s + 2) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(s + 2) equal to 5.477225575 and -5.477225575.

Subproblem 1
s + 2 = 5.477225575

Simplifying
s + 2 = 5.477225575

Reorder the terms:
2 + s = 5.477225575

Solving
2 + s = 5.477225575

Solving for variable 's'.

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

Add '-2' to each side of the equation.
2 + -2 + s = 5.477225575 + -2

Combine like terms: 2 + -2 = 0
0 + s = 5.477225575 + -2
s = 5.477225575 + -2

Combine like terms: 5.477225575 + -2 = 3.477225575
s = 3.477225575

Simplifying
s = 3.477225575

Subproblem 2
s + 2 = -5.477225575

Simplifying
s + 2 = -5.477225575

Reorder the terms:
2 + s = -5.477225575

Solving
2 + s = -5.477225575

Solving for variable 's'.

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

Add '-2' to each side of the equation.
2 + -2 + s = -5.477225575 + -2

Combine like terms: 2 + -2 = 0
0 + s = -5.477225575 + -2
s = -5.477225575 + -2

Combine like terms: -5.477225575 + -2 = -7.477225575
s = -7.477225575

Simplifying
s = -7.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {3.477225575, -7.477225575}
Solution
s = {3.477225575, -7.477225575}