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Simplifying 200 = 0.1s2 + -3s + 22 Reorder the terms: 200 = 22 + -3s + 0.1s2 Solving 200 = 22 + -3s + 0.1s2 Solving for variable 's'. Combine like terms: 200 + -22 = 178 178 + 3s + -0.1s2 = 22 + -3s + 0.1s2 + -22 + 3s + -0.1s2 Reorder the terms: 178 + 3s + -0.1s2 = 22 + -22 + -3s + 3s + 0.1s2 + -0.1s2 Combine like terms: 22 + -22 = 0 178 + 3s + -0.1s2 = 0 + -3s + 3s + 0.1s2 + -0.1s2 178 + 3s + -0.1s2 = -3s + 3s + 0.1s2 + -0.1s2 Combine like terms: -3s + 3s = 0 178 + 3s + -0.1s2 = 0 + 0.1s2 + -0.1s2 178 + 3s + -0.1s2 = 0.1s2 + -0.1s2 Combine like terms: 0.1s2 + -0.1s2 = 0.0 178 + 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'. -1780 + -30s + s2 = 0 Move the constant term to the right: Add '1780' to each side of the equation. -1780 + -30s + 1780 + s2 = 0 + 1780 Reorder the terms: -1780 + 1780 + -30s + s2 = 0 + 1780 Combine like terms: -1780 + 1780 = 0 0 + -30s + s2 = 0 + 1780 -30s + s2 = 0 + 1780 Combine like terms: 0 + 1780 = 1780 -30s + s2 = 1780 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 = 1780 + 225 Reorder the terms: 225 + -30s + s2 = 1780 + 225 Combine like terms: 1780 + 225 = 2005 225 + -30s + s2 = 2005 Factor a perfect square on the left side: (s + -15)(s + -15) = 2005 Calculate the square root of the right side: 44.777226354 Break this problem into two subproblems by setting (s + -15) equal to 44.777226354 and -44.777226354.Subproblem 1
s + -15 = 44.777226354 Simplifying s + -15 = 44.777226354 Reorder the terms: -15 + s = 44.777226354 Solving -15 + s = 44.777226354 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 = 44.777226354 + 15 Combine like terms: -15 + 15 = 0 0 + s = 44.777226354 + 15 s = 44.777226354 + 15 Combine like terms: 44.777226354 + 15 = 59.777226354 s = 59.777226354 Simplifying s = 59.777226354Subproblem 2
s + -15 = -44.777226354 Simplifying s + -15 = -44.777226354 Reorder the terms: -15 + s = -44.777226354 Solving -15 + s = -44.777226354 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 = -44.777226354 + 15 Combine like terms: -15 + 15 = 0 0 + s = -44.777226354 + 15 s = -44.777226354 + 15 Combine like terms: -44.777226354 + 15 = -29.777226354 s = -29.777226354 Simplifying s = -29.777226354Solution
The solution to the problem is based on the solutions from the subproblems. s = {59.777226354, -29.777226354}
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