s^2+10s+14=0

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Solution for s^2+10s+14=0 equation: 


Simplifying
s2 + 10s + 14 = 0

Reorder the terms:
14 + 10s + s2 = 0

Solving
14 + 10s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 10s + -14 + s2 = 0 + -14

Reorder the terms:
14 + -14 + 10s + s2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 10s + s2 = 0 + -14
10s + s2 = 0 + -14

Combine like terms: 0 + -14 = -14
10s + s2 = -14

The s term is 10s.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10s + 25 + s2 = -14 + 25

Reorder the terms:
25 + 10s + s2 = -14 + 25

Combine like terms: -14 + 25 = 11
25 + 10s + s2 = 11

Factor a perfect square on the left side:
(s + 5)(s + 5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(s + 5) equal to 3.31662479 and -3.31662479.


Subproblem 1
s + 5 = 3.31662479

Simplifying
s + 5 = 3.31662479

Reorder the terms:
5 + s = 3.31662479

Solving
5 + s = 3.31662479

Solving for variable 's'.

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

Add '-5' to each side of the equation.
5 + -5 + s = 3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + s = 3.31662479 + -5
s = 3.31662479 + -5

Combine like terms: 3.31662479 + -5 = -1.68337521
s = -1.68337521

Simplifying
s = -1.68337521


Subproblem 2
s + 5 = -3.31662479

Simplifying
s + 5 = -3.31662479

Reorder the terms:
5 + s = -3.31662479

Solving
5 + s = -3.31662479

Solving for variable 's'.

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

Add '-5' to each side of the equation.
5 + -5 + s = -3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + s = -3.31662479 + -5
s = -3.31662479 + -5

Combine like terms: -3.31662479 + -5 = -8.31662479
s = -8.31662479

Simplifying
s = -8.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-1.68337521, -8.31662479}

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