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Simplifying s(s + 0.89) = 92.99 Reorder the terms: s(0.89 + s) = 92.99 (0.89 * s + s * s) = 92.99 (0.89s + s2) = 92.99 Solving 0.89s + s2 = 92.99 Solving for variable 's'. Reorder the terms: -92.99 + 0.89s + s2 = 92.99 + -92.99 Combine like terms: 92.99 + -92.99 = 0.00 -92.99 + 0.89s + s2 = 0.00 Begin completing the square. Move the constant term to the right: Add '92.99' to each side of the equation. -92.99 + 0.89s + 92.99 + s2 = 0.00 + 92.99 Reorder the terms: -92.99 + 92.99 + 0.89s + s2 = 0.00 + 92.99 Combine like terms: -92.99 + 92.99 = 0.00 0.00 + 0.89s + s2 = 0.00 + 92.99 0.89s + s2 = 0.00 + 92.99 Combine like terms: 0.00 + 92.99 = 92.99 0.89s + s2 = 92.99 The s term is 0.89s. Take half its coefficient (0.445). Square it (0.198025) and add it to both sides. Add '0.198025' to each side of the equation. 0.89s + 0.198025 + s2 = 92.99 + 0.198025 Reorder the terms: 0.198025 + 0.89s + s2 = 92.99 + 0.198025 Combine like terms: 92.99 + 0.198025 = 93.188025 0.198025 + 0.89s + s2 = 93.188025 Factor a perfect square on the left side: (s + 0.445)(s + 0.445) = 93.188025 Calculate the square root of the right side: 9.653394481 Break this problem into two subproblems by setting (s + 0.445) equal to 9.653394481 and -9.653394481.Subproblem 1
s + 0.445 = 9.653394481 Simplifying s + 0.445 = 9.653394481 Reorder the terms: 0.445 + s = 9.653394481 Solving 0.445 + s = 9.653394481 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.445' to each side of the equation. 0.445 + -0.445 + s = 9.653394481 + -0.445 Combine like terms: 0.445 + -0.445 = 0.000 0.000 + s = 9.653394481 + -0.445 s = 9.653394481 + -0.445 Combine like terms: 9.653394481 + -0.445 = 9.208394481 s = 9.208394481 Simplifying s = 9.208394481Subproblem 2
s + 0.445 = -9.653394481 Simplifying s + 0.445 = -9.653394481 Reorder the terms: 0.445 + s = -9.653394481 Solving 0.445 + s = -9.653394481 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.445' to each side of the equation. 0.445 + -0.445 + s = -9.653394481 + -0.445 Combine like terms: 0.445 + -0.445 = 0.000 0.000 + s = -9.653394481 + -0.445 s = -9.653394481 + -0.445 Combine like terms: -9.653394481 + -0.445 = -10.098394481 s = -10.098394481 Simplifying s = -10.098394481Solution
The solution to the problem is based on the solutions from the subproblems. s = {9.208394481, -10.098394481}
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