s^2=3+s(7-4s)

Solution for s^2=3+s(7-4s) equation:

Simplifying
s2 = 3 + s(7 + -4s)
s2 = 3 + (7 * s + -4s * s)
s2 = 3 + (7s + -4s2)

Solving
s2 = 3 + 7s + -4s2

Solving for variable 's'.

Reorder the terms:
-3 + -7s + s2 + 4s2 = 3 + 7s + -4s2 + -3 + -7s + 4s2

Combine like terms: s2 + 4s2 = 5s2
-3 + -7s + 5s2 = 3 + 7s + -4s2 + -3 + -7s + 4s2

Reorder the terms:
-3 + -7s + 5s2 = 3 + -3 + 7s + -7s + -4s2 + 4s2

Combine like terms: 3 + -3 = 0
-3 + -7s + 5s2 = 0 + 7s + -7s + -4s2 + 4s2
-3 + -7s + 5s2 = 7s + -7s + -4s2 + 4s2

Combine like terms: 7s + -7s = 0
-3 + -7s + 5s2 = 0 + -4s2 + 4s2
-3 + -7s + 5s2 = -4s2 + 4s2

Combine like terms: -4s2 + 4s2 = 0
-3 + -7s + 5s2 = 0

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

Divide each side by '5'.
-0.6 + -1.4s + s2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1.4s + 0.6 + s2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1.4s + s2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -1.4s + s2 = 0 + 0.6
-1.4s + s2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-1.4s + s2 = 0.6

The s term is -1.4s.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4s + 0.49 + s2 = 0.6 + 0.49

Reorder the terms:
0.49 + -1.4s + s2 = 0.6 + 0.49

Combine like terms: 0.6 + 0.49 = 1.09
0.49 + -1.4s + s2 = 1.09

Factor a perfect square on the left side:
(s + -0.7)(s + -0.7) = 1.09

Calculate the square root of the right side: 1.044030651

Break this problem into two subproblems by setting 
(s + -0.7) equal to 1.044030651 and -1.044030651.

Subproblem 1
s + -0.7 = 1.044030651

Simplifying
s + -0.7 = 1.044030651

Reorder the terms:
-0.7 + s = 1.044030651

Solving
-0.7 + s = 1.044030651

Solving for variable 's'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + s = 1.044030651 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + s = 1.044030651 + 0.7
s = 1.044030651 + 0.7

Combine like terms: 1.044030651 + 0.7 = 1.744030651
s = 1.744030651

Simplifying
s = 1.744030651

Subproblem 2
s + -0.7 = -1.044030651

Simplifying
s + -0.7 = -1.044030651

Reorder the terms:
-0.7 + s = -1.044030651

Solving
-0.7 + s = -1.044030651

Solving for variable 's'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + s = -1.044030651 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + s = -1.044030651 + 0.7
s = -1.044030651 + 0.7

Combine like terms: -1.044030651 + 0.7 = -0.344030651
s = -0.344030651

Simplifying
s = -0.344030651

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {1.744030651, -0.344030651}