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Simplifying 0.1s2 + -3s + 22 = 2000 Reorder the terms: 22 + -3s + 0.1s2 = 2000 Solving 22 + -3s + 0.1s2 = 2000 Solving for variable 's'. Reorder the terms: 22 + -2000 + -3s + 0.1s2 = 2000 + -2000 Combine like terms: 22 + -2000 = -1978 -1978 + -3s + 0.1s2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -1978 + -3s + 0.1s2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -19780 + -30s + s2 = 0 Move the constant term to the right: Add '19780' to each side of the equation. -19780 + -30s + 19780 + s2 = 0 + 19780 Reorder the terms: -19780 + 19780 + -30s + s2 = 0 + 19780 Combine like terms: -19780 + 19780 = 0 0 + -30s + s2 = 0 + 19780 -30s + s2 = 0 + 19780 Combine like terms: 0 + 19780 = 19780 -30s + s2 = 19780 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 = 19780 + 225 Reorder the terms: 225 + -30s + s2 = 19780 + 225 Combine like terms: 19780 + 225 = 20005 225 + -30s + s2 = 20005 Factor a perfect square on the left side: (s + -15)(s + -15) = 20005 Calculate the square root of the right side: 141.439032802 Break this problem into two subproblems by setting (s + -15) equal to 141.439032802 and -141.439032802.Subproblem 1
s + -15 = 141.439032802 Simplifying s + -15 = 141.439032802 Reorder the terms: -15 + s = 141.439032802 Solving -15 + s = 141.439032802 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 = 141.439032802 + 15 Combine like terms: -15 + 15 = 0 0 + s = 141.439032802 + 15 s = 141.439032802 + 15 Combine like terms: 141.439032802 + 15 = 156.439032802 s = 156.439032802 Simplifying s = 156.439032802Subproblem 2
s + -15 = -141.439032802 Simplifying s + -15 = -141.439032802 Reorder the terms: -15 + s = -141.439032802 Solving -15 + s = -141.439032802 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 = -141.439032802 + 15 Combine like terms: -15 + 15 = 0 0 + s = -141.439032802 + 15 s = -141.439032802 + 15 Combine like terms: -141.439032802 + 15 = -126.439032802 s = -126.439032802 Simplifying s = -126.439032802Solution
The solution to the problem is based on the solutions from the subproblems. s = {156.439032802, -126.439032802}
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