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Simplifying 0.0000000002s2 + 0.000000001s + -4 = 0 Reorder the terms: -4 + 0.000000001s + 0.0000000002s2 = 0 Solving -4 + 0.000000001s + 0.0000000002s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 0.0000000002 the coefficient of the squared term: Divide each side by '0.0000000002'. -20000000000 + 5s + s2 = 0 Move the constant term to the right: Add '20000000000' to each side of the equation. -20000000000 + 5s + 20000000000 + s2 = 0 + 20000000000 Reorder the terms: -20000000000 + 20000000000 + 5s + s2 = 0 + 20000000000 Combine like terms: -20000000000 + 20000000000 = 0 0 + 5s + s2 = 0 + 20000000000 5s + s2 = 0 + 20000000000 Combine like terms: 0 + 20000000000 = 20000000000 5s + s2 = 20000000000 The s term is 5s. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5s + 6.25 + s2 = 20000000000 + 6.25 Reorder the terms: 6.25 + 5s + s2 = 20000000000 + 6.25 Combine like terms: 20000000000 + 6.25 = 20000000006.25 6.25 + 5s + s2 = 20000000006.25 Factor a perfect square on the left side: (s + 2.5)(s + 2.5) = 20000000006.25 Calculate the square root of the right side: 141421.356259407 Break this problem into two subproblems by setting (s + 2.5) equal to 141421.356259407 and -141421.356259407.Subproblem 1
s + 2.5 = 141421.356259407 Simplifying s + 2.5 = 141421.356259407 Reorder the terms: 2.5 + s = 141421.356259407 Solving 2.5 + s = 141421.356259407 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + s = 141421.356259407 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = 141421.356259407 + -2.5 s = 141421.356259407 + -2.5 Combine like terms: 141421.356259407 + -2.5 = 141418.856259407 s = 141418.856259407 Simplifying s = 141418.856259407Subproblem 2
s + 2.5 = -141421.356259407 Simplifying s + 2.5 = -141421.356259407 Reorder the terms: 2.5 + s = -141421.356259407 Solving 2.5 + s = -141421.356259407 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + s = -141421.356259407 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = -141421.356259407 + -2.5 s = -141421.356259407 + -2.5 Combine like terms: -141421.356259407 + -2.5 = -141423.856259407 s = -141423.856259407 Simplifying s = -141423.856259407Solution
The solution to the problem is based on the solutions from the subproblems. s = {141418.856259407, -141423.856259407}
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