30=.7s^2+.5s

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Solution for 30=.7s^2+.5s equation:


Simplifying
30 = 0.7s2 + 0.5s

Reorder the terms:
30 = 0.5s + 0.7s2

Solving
30 = 0.5s + 0.7s2

Solving for variable 's'.

Reorder the terms:
30 + -0.5s + -0.7s2 = 0.5s + -0.5s + 0.7s2 + -0.7s2

Combine like terms: 0.5s + -0.5s = 0.0
30 + -0.5s + -0.7s2 = 0.0 + 0.7s2 + -0.7s2
30 + -0.5s + -0.7s2 = 0.7s2 + -0.7s2

Combine like terms: 0.7s2 + -0.7s2 = 0.0
30 + -0.5s + -0.7s2 = 0.0

Begin completing the square.  Divide all terms by
-0.7 the coefficient of the squared term: 

Divide each side by '-0.7'.
-42.85714286 + 0.7142857143s + s2 = 0

Move the constant term to the right:

Add '42.85714286' to each side of the equation.
-42.85714286 + 0.7142857143s + 42.85714286 + s2 = 0 + 42.85714286

Reorder the terms:
-42.85714286 + 42.85714286 + 0.7142857143s + s2 = 0 + 42.85714286

Combine like terms: -42.85714286 + 42.85714286 = 0.00000000
0.00000000 + 0.7142857143s + s2 = 0 + 42.85714286
0.7142857143s + s2 = 0 + 42.85714286

Combine like terms: 0 + 42.85714286 = 42.85714286
0.7142857143s + s2 = 42.85714286

The s term is 0.7142857143s.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143s + 0.1275510204 + s2 = 42.85714286 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143s + s2 = 42.85714286 + 0.1275510204

Combine like terms: 42.85714286 + 0.1275510204 = 42.9846938804
0.1275510204 + 0.7142857143s + s2 = 42.9846938804

Factor a perfect square on the left side:
(s + 0.3571428572)(s + 0.3571428572) = 42.9846938804

Calculate the square root of the right side: 6.55627134

Break this problem into two subproblems by setting 
(s + 0.3571428572) equal to 6.55627134 and -6.55627134.

Subproblem 1

s + 0.3571428572 = 6.55627134 Simplifying s + 0.3571428572 = 6.55627134 Reorder the terms: 0.3571428572 + s = 6.55627134 Solving 0.3571428572 + s = 6.55627134 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + s = 6.55627134 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + s = 6.55627134 + -0.3571428572 s = 6.55627134 + -0.3571428572 Combine like terms: 6.55627134 + -0.3571428572 = 6.1991284828 s = 6.1991284828 Simplifying s = 6.1991284828

Subproblem 2

s + 0.3571428572 = -6.55627134 Simplifying s + 0.3571428572 = -6.55627134 Reorder the terms: 0.3571428572 + s = -6.55627134 Solving 0.3571428572 + s = -6.55627134 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + s = -6.55627134 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + s = -6.55627134 + -0.3571428572 s = -6.55627134 + -0.3571428572 Combine like terms: -6.55627134 + -0.3571428572 = -6.9134141972 s = -6.9134141972 Simplifying s = -6.9134141972

Solution

The solution to the problem is based on the solutions from the subproblems. s = {6.1991284828, -6.9134141972}

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