25s^2+30s=9

Solution for 25s^2+30s=9 equation:

Simplifying
25s2 + 30s = 9

Reorder the terms:
30s + 25s2 = 9

Solving
30s + 25s2 = 9

Solving for variable 's'.

Reorder the terms:
-9 + 30s + 25s2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 30s + 25s2 = 0

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

Divide each side by '25'.
-0.36 + 1.2s + s2 = 0

Move the constant term to the right:

Add '0.36' to each side of the equation.
-0.36 + 1.2s + 0.36 + s2 = 0 + 0.36

Reorder the terms:
-0.36 + 0.36 + 1.2s + s2 = 0 + 0.36

Combine like terms: -0.36 + 0.36 = 0.00
0.00 + 1.2s + s2 = 0 + 0.36
1.2s + s2 = 0 + 0.36

Combine like terms: 0 + 0.36 = 0.36
1.2s + s2 = 0.36

The s term is 1.2s.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2s + 0.36 + s2 = 0.36 + 0.36

Reorder the terms:
0.36 + 1.2s + s2 = 0.36 + 0.36

Combine like terms: 0.36 + 0.36 = 0.72
0.36 + 1.2s + s2 = 0.72

Factor a perfect square on the left side:
(s + 0.6)(s + 0.6) = 0.72

Calculate the square root of the right side: 0.848528137

Break this problem into two subproblems by setting 
(s + 0.6) equal to 0.848528137 and -0.848528137.

Subproblem 1
s + 0.6 = 0.848528137

Simplifying
s + 0.6 = 0.848528137

Reorder the terms:
0.6 + s = 0.848528137

Solving
0.6 + s = 0.848528137

Solving for variable 's'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + s = 0.848528137 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + s = 0.848528137 + -0.6
s = 0.848528137 + -0.6

Combine like terms: 0.848528137 + -0.6 = 0.248528137
s = 0.248528137

Simplifying
s = 0.248528137

Subproblem 2
s + 0.6 = -0.848528137

Simplifying
s + 0.6 = -0.848528137

Reorder the terms:
0.6 + s = -0.848528137

Solving
0.6 + s = -0.848528137

Solving for variable 's'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + s = -0.848528137 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + s = -0.848528137 + -0.6
s = -0.848528137 + -0.6

Combine like terms: -0.848528137 + -0.6 = -1.448528137
s = -1.448528137

Simplifying
s = -1.448528137

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.248528137, -1.448528137}