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Simplifying 0.01s2 + 0.8s + 3.4 = 0 Reorder the terms: 3.4 + 0.8s + 0.01s2 = 0 Solving 3.4 + 0.8s + 0.01s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 340 + 80s + s2 = 0 Move the constant term to the right: Add '-340' to each side of the equation. 340 + 80s + -340 + s2 = 0 + -340 Reorder the terms: 340 + -340 + 80s + s2 = 0 + -340 Combine like terms: 340 + -340 = 0 0 + 80s + s2 = 0 + -340 80s + s2 = 0 + -340 Combine like terms: 0 + -340 = -340 80s + s2 = -340 The s term is 80s. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80s + 1600 + s2 = -340 + 1600 Reorder the terms: 1600 + 80s + s2 = -340 + 1600 Combine like terms: -340 + 1600 = 1260 1600 + 80s + s2 = 1260 Factor a perfect square on the left side: (s + 40)(s + 40) = 1260 Calculate the square root of the right side: 35.496478699 Break this problem into two subproblems by setting (s + 40) equal to 35.496478699 and -35.496478699.Subproblem 1
s + 40 = 35.496478699 Simplifying s + 40 = 35.496478699 Reorder the terms: 40 + s = 35.496478699 Solving 40 + s = 35.496478699 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + s = 35.496478699 + -40 Combine like terms: 40 + -40 = 0 0 + s = 35.496478699 + -40 s = 35.496478699 + -40 Combine like terms: 35.496478699 + -40 = -4.503521301 s = -4.503521301 Simplifying s = -4.503521301Subproblem 2
s + 40 = -35.496478699 Simplifying s + 40 = -35.496478699 Reorder the terms: 40 + s = -35.496478699 Solving 40 + s = -35.496478699 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + s = -35.496478699 + -40 Combine like terms: 40 + -40 = 0 0 + s = -35.496478699 + -40 s = -35.496478699 + -40 Combine like terms: -35.496478699 + -40 = -75.496478699 s = -75.496478699 Simplifying s = -75.496478699Solution
The solution to the problem is based on the solutions from the subproblems. s = {-4.503521301, -75.496478699}
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