0=0.1s^2-3s-2228

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Solution for 0=0.1s^2-3s-2228 equation:


Simplifying
0 = 0.1s2 + -3s + -2228

Reorder the terms:
0 = -2228 + -3s + 0.1s2

Solving
0 = -2228 + -3s + 0.1s2

Solving for variable 's'.

Combine like terms: 0 + 2228 = 2228
2228 + 3s + -0.1s2 = -2228 + -3s + 0.1s2 + 2228 + 3s + -0.1s2

Reorder the terms:
2228 + 3s + -0.1s2 = -2228 + 2228 + -3s + 3s + 0.1s2 + -0.1s2

Combine like terms: -2228 + 2228 = 0
2228 + 3s + -0.1s2 = 0 + -3s + 3s + 0.1s2 + -0.1s2
2228 + 3s + -0.1s2 = -3s + 3s + 0.1s2 + -0.1s2

Combine like terms: -3s + 3s = 0
2228 + 3s + -0.1s2 = 0 + 0.1s2 + -0.1s2
2228 + 3s + -0.1s2 = 0.1s2 + -0.1s2

Combine like terms: 0.1s2 + -0.1s2 = 0.0
2228 + 3s + -0.1s2 = 0.0

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
-22280 + -30s + s2 = 0

Move the constant term to the right:

Add '22280' to each side of the equation.
-22280 + -30s + 22280 + s2 = 0 + 22280

Reorder the terms:
-22280 + 22280 + -30s + s2 = 0 + 22280

Combine like terms: -22280 + 22280 = 0
0 + -30s + s2 = 0 + 22280
-30s + s2 = 0 + 22280

Combine like terms: 0 + 22280 = 22280
-30s + s2 = 22280

The s term is -30s.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30s + 225 + s2 = 22280 + 225

Reorder the terms:
225 + -30s + s2 = 22280 + 225

Combine like terms: 22280 + 225 = 22505
225 + -30s + s2 = 22505

Factor a perfect square on the left side:
(s + -15)(s + -15) = 22505

Calculate the square root of the right side: 150.016665741

Break this problem into two subproblems by setting 
(s + -15) equal to 150.016665741 and -150.016665741.

Subproblem 1

s + -15 = 150.016665741 Simplifying s + -15 = 150.016665741 Reorder the terms: -15 + s = 150.016665741 Solving -15 + s = 150.016665741 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + s = 150.016665741 + 15 Combine like terms: -15 + 15 = 0 0 + s = 150.016665741 + 15 s = 150.016665741 + 15 Combine like terms: 150.016665741 + 15 = 165.016665741 s = 165.016665741 Simplifying s = 165.016665741

Subproblem 2

s + -15 = -150.016665741 Simplifying s + -15 = -150.016665741 Reorder the terms: -15 + s = -150.016665741 Solving -15 + s = -150.016665741 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + s = -150.016665741 + 15 Combine like terms: -15 + 15 = 0 0 + s = -150.016665741 + 15 s = -150.016665741 + 15 Combine like terms: -150.016665741 + 15 = -135.016665741 s = -135.016665741 Simplifying s = -135.016665741

Solution

The solution to the problem is based on the solutions from the subproblems. s = {165.016665741, -135.016665741}

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