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Simplifying 98s2 + 648s + -5881 = 0 Reorder the terms: -5881 + 648s + 98s2 = 0 Solving -5881 + 648s + 98s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 98 the coefficient of the squared term: Divide each side by '98'. -60.01020408 + 6.612244898s + s2 = 0 Move the constant term to the right: Add '60.01020408' to each side of the equation. -60.01020408 + 6.612244898s + 60.01020408 + s2 = 0 + 60.01020408 Reorder the terms: -60.01020408 + 60.01020408 + 6.612244898s + s2 = 0 + 60.01020408 Combine like terms: -60.01020408 + 60.01020408 = 0.00000000 0.00000000 + 6.612244898s + s2 = 0 + 60.01020408 6.612244898s + s2 = 0 + 60.01020408 Combine like terms: 0 + 60.01020408 = 60.01020408 6.612244898s + s2 = 60.01020408 The s term is 6.612244898s. Take half its coefficient (3.306122449). Square it (10.93044565) and add it to both sides. Add '10.93044565' to each side of the equation. 6.612244898s + 10.93044565 + s2 = 60.01020408 + 10.93044565 Reorder the terms: 10.93044565 + 6.612244898s + s2 = 60.01020408 + 10.93044565 Combine like terms: 60.01020408 + 10.93044565 = 70.94064973 10.93044565 + 6.612244898s + s2 = 70.94064973 Factor a perfect square on the left side: (s + 3.306122449)(s + 3.306122449) = 70.94064973 Calculate the square root of the right side: 8.422627246 Break this problem into two subproblems by setting (s + 3.306122449) equal to 8.422627246 and -8.422627246.Subproblem 1
s + 3.306122449 = 8.422627246 Simplifying s + 3.306122449 = 8.422627246 Reorder the terms: 3.306122449 + s = 8.422627246 Solving 3.306122449 + s = 8.422627246 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.306122449' to each side of the equation. 3.306122449 + -3.306122449 + s = 8.422627246 + -3.306122449 Combine like terms: 3.306122449 + -3.306122449 = 0.000000000 0.000000000 + s = 8.422627246 + -3.306122449 s = 8.422627246 + -3.306122449 Combine like terms: 8.422627246 + -3.306122449 = 5.116504797 s = 5.116504797 Simplifying s = 5.116504797Subproblem 2
s + 3.306122449 = -8.422627246 Simplifying s + 3.306122449 = -8.422627246 Reorder the terms: 3.306122449 + s = -8.422627246 Solving 3.306122449 + s = -8.422627246 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.306122449' to each side of the equation. 3.306122449 + -3.306122449 + s = -8.422627246 + -3.306122449 Combine like terms: 3.306122449 + -3.306122449 = 0.000000000 0.000000000 + s = -8.422627246 + -3.306122449 s = -8.422627246 + -3.306122449 Combine like terms: -8.422627246 + -3.306122449 = -11.728749695 s = -11.728749695 Simplifying s = -11.728749695Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.116504797, -11.728749695}
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