s^2=9+s(5-7s)

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Solution for s^2=9+s(5-7s) equation:


Simplifying
s2 = 9 + s(5 + -7s)
s2 = 9 + (5 * s + -7s * s)
s2 = 9 + (5s + -7s2)

Solving
s2 = 9 + 5s + -7s2

Solving for variable 's'.

Reorder the terms:
-9 + -5s + s2 + 7s2 = 9 + 5s + -7s2 + -9 + -5s + 7s2

Combine like terms: s2 + 7s2 = 8s2
-9 + -5s + 8s2 = 9 + 5s + -7s2 + -9 + -5s + 7s2

Reorder the terms:
-9 + -5s + 8s2 = 9 + -9 + 5s + -5s + -7s2 + 7s2

Combine like terms: 9 + -9 = 0
-9 + -5s + 8s2 = 0 + 5s + -5s + -7s2 + 7s2
-9 + -5s + 8s2 = 5s + -5s + -7s2 + 7s2

Combine like terms: 5s + -5s = 0
-9 + -5s + 8s2 = 0 + -7s2 + 7s2
-9 + -5s + 8s2 = -7s2 + 7s2

Combine like terms: -7s2 + 7s2 = 0
-9 + -5s + 8s2 = 0

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

Divide each side by '8'.
-1.125 + -0.625s + s2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -0.625s + 1.125 + s2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -0.625s + s2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -0.625s + s2 = 0 + 1.125
-0.625s + s2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-0.625s + s2 = 1.125

The s term is -0.625s.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625s + 0.09765625 + s2 = 1.125 + 0.09765625

Reorder the terms:
0.09765625 + -0.625s + s2 = 1.125 + 0.09765625

Combine like terms: 1.125 + 0.09765625 = 1.22265625
0.09765625 + -0.625s + s2 = 1.22265625

Factor a perfect square on the left side:
(s + -0.3125)(s + -0.3125) = 1.22265625

Calculate the square root of the right side: 1.105737876

Break this problem into two subproblems by setting 
(s + -0.3125) equal to 1.105737876 and -1.105737876.

Subproblem 1

s + -0.3125 = 1.105737876 Simplifying s + -0.3125 = 1.105737876 Reorder the terms: -0.3125 + s = 1.105737876 Solving -0.3125 + s = 1.105737876 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + s = 1.105737876 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + s = 1.105737876 + 0.3125 s = 1.105737876 + 0.3125 Combine like terms: 1.105737876 + 0.3125 = 1.418237876 s = 1.418237876 Simplifying s = 1.418237876

Subproblem 2

s + -0.3125 = -1.105737876 Simplifying s + -0.3125 = -1.105737876 Reorder the terms: -0.3125 + s = -1.105737876 Solving -0.3125 + s = -1.105737876 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + s = -1.105737876 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + s = -1.105737876 + 0.3125 s = -1.105737876 + 0.3125 Combine like terms: -1.105737876 + 0.3125 = -0.793237876 s = -0.793237876 Simplifying s = -0.793237876

Solution

The solution to the problem is based on the solutions from the subproblems. s = {1.418237876, -0.793237876}

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