2400=0.1s^2-3s+22

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Solution for 2400=0.1s^2-3s+22 equation:


Simplifying
2400 = 0.1s2 + -3s + 22

Reorder the terms:
2400 = 22 + -3s + 0.1s2

Solving
2400 = 22 + -3s + 0.1s2

Solving for variable 's'.

Combine like terms: 2400 + -22 = 2378
2378 + 3s + -0.1s2 = 22 + -3s + 0.1s2 + -22 + 3s + -0.1s2

Reorder the terms:
2378 + 3s + -0.1s2 = 22 + -22 + -3s + 3s + 0.1s2 + -0.1s2

Combine like terms: 22 + -22 = 0
2378 + 3s + -0.1s2 = 0 + -3s + 3s + 0.1s2 + -0.1s2
2378 + 3s + -0.1s2 = -3s + 3s + 0.1s2 + -0.1s2

Combine like terms: -3s + 3s = 0
2378 + 3s + -0.1s2 = 0 + 0.1s2 + -0.1s2
2378 + 3s + -0.1s2 = 0.1s2 + -0.1s2

Combine like terms: 0.1s2 + -0.1s2 = 0.0
2378 + 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'.
-23780 + -30s + s2 = 0

Move the constant term to the right:

Add '23780' to each side of the equation.
-23780 + -30s + 23780 + s2 = 0 + 23780

Reorder the terms:
-23780 + 23780 + -30s + s2 = 0 + 23780

Combine like terms: -23780 + 23780 = 0
0 + -30s + s2 = 0 + 23780
-30s + s2 = 0 + 23780

Combine like terms: 0 + 23780 = 23780
-30s + s2 = 23780

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 = 23780 + 225

Reorder the terms:
225 + -30s + s2 = 23780 + 225

Combine like terms: 23780 + 225 = 24005
225 + -30s + s2 = 24005

Factor a perfect square on the left side:
(s + -15)(s + -15) = 24005

Calculate the square root of the right side: 154.935470439

Break this problem into two subproblems by setting 
(s + -15) equal to 154.935470439 and -154.935470439.

Subproblem 1

s + -15 = 154.935470439 Simplifying s + -15 = 154.935470439 Reorder the terms: -15 + s = 154.935470439 Solving -15 + s = 154.935470439 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 = 154.935470439 + 15 Combine like terms: -15 + 15 = 0 0 + s = 154.935470439 + 15 s = 154.935470439 + 15 Combine like terms: 154.935470439 + 15 = 169.935470439 s = 169.935470439 Simplifying s = 169.935470439

Subproblem 2

s + -15 = -154.935470439 Simplifying s + -15 = -154.935470439 Reorder the terms: -15 + s = -154.935470439 Solving -15 + s = -154.935470439 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 = -154.935470439 + 15 Combine like terms: -15 + 15 = 0 0 + s = -154.935470439 + 15 s = -154.935470439 + 15 Combine like terms: -154.935470439 + 15 = -139.935470439 s = -139.935470439 Simplifying s = -139.935470439

Solution

The solution to the problem is based on the solutions from the subproblems. s = {169.935470439, -139.935470439}

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