2s^2+44s-58=0

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Solution for 2s^2+44s-58=0 equation: 


Simplifying
2s2 + 44s + -58 = 0

Reorder the terms:
-58 + 44s + 2s2 = 0

Solving
-58 + 44s + 2s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-29 + 22s + s2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-29 + 22s + s2)' equal to zero and attempt to solve:

Simplifying
-29 + 22s + s2 = 0

Solving
-29 + 22s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 22s + 29 + s2 = 0 + 29

Reorder the terms:
-29 + 29 + 22s + s2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 22s + s2 = 0 + 29
22s + s2 = 0 + 29

Combine like terms: 0 + 29 = 29
22s + s2 = 29

The s term is 22s.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22s + 121 + s2 = 29 + 121

Reorder the terms:
121 + 22s + s2 = 29 + 121

Combine like terms: 29 + 121 = 150
121 + 22s + s2 = 150

Factor a perfect square on the left side:
(s + 11)(s + 11) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(s + 11) equal to 12.247448714 and -12.247448714.


Subproblem 1
s + 11 = 12.247448714

Simplifying
s + 11 = 12.247448714

Reorder the terms:
11 + s = 12.247448714

Solving
11 + s = 12.247448714

Solving for variable 's'.

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

Add '-11' to each side of the equation.
11 + -11 + s = 12.247448714 + -11

Combine like terms: 11 + -11 = 0
0 + s = 12.247448714 + -11
s = 12.247448714 + -11

Combine like terms: 12.247448714 + -11 = 1.247448714
s = 1.247448714

Simplifying
s = 1.247448714


Subproblem 2
s + 11 = -12.247448714

Simplifying
s + 11 = -12.247448714

Reorder the terms:
11 + s = -12.247448714

Solving
11 + s = -12.247448714

Solving for variable 's'.

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

Add '-11' to each side of the equation.
11 + -11 + s = -12.247448714 + -11

Combine like terms: 11 + -11 = 0
0 + s = -12.247448714 + -11
s = -12.247448714 + -11

Combine like terms: -12.247448714 + -11 = -23.247448714
s = -23.247448714

Simplifying
s = -23.247448714


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {1.247448714, -23.247448714}
Solution
s = {1.247448714, -23.247448714}

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