65=0.05s^2+1.1s

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Solution for 65=0.05s^2+1.1s equation:


Simplifying
65 = 0.05s2 + 1.1s

Reorder the terms:
65 = 1.1s + 0.05s2

Solving
65 = 1.1s + 0.05s2

Solving for variable 's'.

Reorder the terms:
65 + -1.1s + -0.05s2 = 1.1s + -1.1s + 0.05s2 + -0.05s2

Combine like terms: 1.1s + -1.1s = 0.0
65 + -1.1s + -0.05s2 = 0.0 + 0.05s2 + -0.05s2
65 + -1.1s + -0.05s2 = 0.05s2 + -0.05s2

Combine like terms: 0.05s2 + -0.05s2 = 0.00
65 + -1.1s + -0.05s2 = 0.00

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
-1300 + 22s + s2 = 0

Move the constant term to the right:

Add '1300' to each side of the equation.
-1300 + 22s + 1300 + s2 = 0 + 1300

Reorder the terms:
-1300 + 1300 + 22s + s2 = 0 + 1300

Combine like terms: -1300 + 1300 = 0
0 + 22s + s2 = 0 + 1300
22s + s2 = 0 + 1300

Combine like terms: 0 + 1300 = 1300
22s + s2 = 1300

The s term is 22s.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22s + 121 + s2 = 1300 + 121

Reorder the terms:
121 + 22s + s2 = 1300 + 121

Combine like terms: 1300 + 121 = 1421
121 + 22s + s2 = 1421

Factor a perfect square on the left side:
(s + 11)(s + 11) = 1421

Calculate the square root of the right side: 37.69615365

Break this problem into two subproblems by setting 
(s + 11) equal to 37.69615365 and -37.69615365.

Subproblem 1

s + 11 = 37.69615365 Simplifying s + 11 = 37.69615365 Reorder the terms: 11 + s = 37.69615365 Solving 11 + s = 37.69615365 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + s = 37.69615365 + -11 Combine like terms: 11 + -11 = 0 0 + s = 37.69615365 + -11 s = 37.69615365 + -11 Combine like terms: 37.69615365 + -11 = 26.69615365 s = 26.69615365 Simplifying s = 26.69615365

Subproblem 2

s + 11 = -37.69615365 Simplifying s + 11 = -37.69615365 Reorder the terms: 11 + s = -37.69615365 Solving 11 + s = -37.69615365 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + s = -37.69615365 + -11 Combine like terms: 11 + -11 = 0 0 + s = -37.69615365 + -11 s = -37.69615365 + -11 Combine like terms: -37.69615365 + -11 = -48.69615365 s = -48.69615365 Simplifying s = -48.69615365

Solution

The solution to the problem is based on the solutions from the subproblems. s = {26.69615365, -48.69615365}

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