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Simplifying -1s2 + -20s + 240 = 0 Reorder the terms: 240 + -20s + -1s2 = 0 Solving 240 + -20s + -1s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -240 + 20s + s2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + 20s + 240 + s2 = 0 + 240 Reorder the terms: -240 + 240 + 20s + s2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 20s + s2 = 0 + 240 20s + s2 = 0 + 240 Combine like terms: 0 + 240 = 240 20s + s2 = 240 The s term is 20s. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20s + 100 + s2 = 240 + 100 Reorder the terms: 100 + 20s + s2 = 240 + 100 Combine like terms: 240 + 100 = 340 100 + 20s + s2 = 340 Factor a perfect square on the left side: (s + 10)(s + 10) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (s + 10) equal to 18.439088915 and -18.439088915.Subproblem 1
s + 10 = 18.439088915 Simplifying s + 10 = 18.439088915 Reorder the terms: 10 + s = 18.439088915 Solving 10 + s = 18.439088915 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + s = 18.439088915 + -10 Combine like terms: 10 + -10 = 0 0 + s = 18.439088915 + -10 s = 18.439088915 + -10 Combine like terms: 18.439088915 + -10 = 8.439088915 s = 8.439088915 Simplifying s = 8.439088915Subproblem 2
s + 10 = -18.439088915 Simplifying s + 10 = -18.439088915 Reorder the terms: 10 + s = -18.439088915 Solving 10 + s = -18.439088915 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + s = -18.439088915 + -10 Combine like terms: 10 + -10 = 0 0 + s = -18.439088915 + -10 s = -18.439088915 + -10 Combine like terms: -18.439088915 + -10 = -28.439088915 s = -28.439088915 Simplifying s = -28.439088915Solution
The solution to the problem is based on the solutions from the subproblems. s = {8.439088915, -28.439088915}
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