5s^2-14s-3=3

Solution for 5s^2-14s-3=3 equation:

Simplifying
5s2 + -14s + -3 = 3

Reorder the terms:
-3 + -14s + 5s2 = 3

Solving
-3 + -14s + 5s2 = 3

Solving for variable 's'.

Reorder the terms:
-3 + -3 + -14s + 5s2 = 3 + -3

Combine like terms: -3 + -3 = -6
-6 + -14s + 5s2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + -14s + 5s2 = 0

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

Divide each side by '5'.
-1.2 + -2.8s + s2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -2.8s + 1.2 + s2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -2.8s + s2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -2.8s + s2 = 0 + 1.2
-2.8s + s2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-2.8s + s2 = 1.2

The s term is -2.8s.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8s + 1.96 + s2 = 1.2 + 1.96

Reorder the terms:
1.96 + -2.8s + s2 = 1.2 + 1.96

Combine like terms: 1.2 + 1.96 = 3.16
1.96 + -2.8s + s2 = 3.16

Factor a perfect square on the left side:
(s + -1.4)(s + -1.4) = 3.16

Calculate the square root of the right side: 1.777638883

Break this problem into two subproblems by setting 
(s + -1.4) equal to 1.777638883 and -1.777638883.

Subproblem 1
s + -1.4 = 1.777638883

Simplifying
s + -1.4 = 1.777638883

Reorder the terms:
-1.4 + s = 1.777638883

Solving
-1.4 + s = 1.777638883

Solving for variable 's'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + s = 1.777638883 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + s = 1.777638883 + 1.4
s = 1.777638883 + 1.4

Combine like terms: 1.777638883 + 1.4 = 3.177638883
s = 3.177638883

Simplifying
s = 3.177638883

Subproblem 2
s + -1.4 = -1.777638883

Simplifying
s + -1.4 = -1.777638883

Reorder the terms:
-1.4 + s = -1.777638883

Solving
-1.4 + s = -1.777638883

Solving for variable 's'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + s = -1.777638883 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + s = -1.777638883 + 1.4
s = -1.777638883 + 1.4

Combine like terms: -1.777638883 + 1.4 = -0.377638883
s = -0.377638883

Simplifying
s = -0.377638883

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {3.177638883, -0.377638883}