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Simplifying (s + 2) * 2s + 4 = 43.2 Reorder the terms: (2 + s) * 2s + 4 = 43.2 Reorder the terms for easier multiplication: 2s(2 + s) + 4 = 43.2 (2 * 2s + s * 2s) + 4 = 43.2 (4s + 2s2) + 4 = 43.2 Reorder the terms: 4 + 4s + 2s2 = 43.2 Solving 4 + 4s + 2s2 = 43.2 Solving for variable 's'. Reorder the terms: 4 + -43.2 + 4s + 2s2 = 43.2 + -43.2 Combine like terms: 4 + -43.2 = -39.2 -39.2 + 4s + 2s2 = 43.2 + -43.2 Combine like terms: 43.2 + -43.2 = 0.0 -39.2 + 4s + 2s2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19.6 + 2s + s2 = 0.0 Move the constant term to the right: Add '19.6' to each side of the equation. -19.6 + 2s + 19.6 + s2 = 0.0 + 19.6 Reorder the terms: -19.6 + 19.6 + 2s + s2 = 0.0 + 19.6 Combine like terms: -19.6 + 19.6 = 0.0 0.0 + 2s + s2 = 0.0 + 19.6 2s + s2 = 0.0 + 19.6 Combine like terms: 0.0 + 19.6 = 19.6 2s + s2 = 19.6 The s term is 2s. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2s + 1 + s2 = 19.6 + 1 Reorder the terms: 1 + 2s + s2 = 19.6 + 1 Combine like terms: 19.6 + 1 = 20.6 1 + 2s + s2 = 20.6 Factor a perfect square on the left side: (s + 1)(s + 1) = 20.6 Calculate the square root of the right side: 4.538722287 Break this problem into two subproblems by setting (s + 1) equal to 4.538722287 and -4.538722287.Subproblem 1
s + 1 = 4.538722287 Simplifying s + 1 = 4.538722287 Reorder the terms: 1 + s = 4.538722287 Solving 1 + s = 4.538722287 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = 4.538722287 + -1 Combine like terms: 1 + -1 = 0 0 + s = 4.538722287 + -1 s = 4.538722287 + -1 Combine like terms: 4.538722287 + -1 = 3.538722287 s = 3.538722287 Simplifying s = 3.538722287Subproblem 2
s + 1 = -4.538722287 Simplifying s + 1 = -4.538722287 Reorder the terms: 1 + s = -4.538722287 Solving 1 + s = -4.538722287 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = -4.538722287 + -1 Combine like terms: 1 + -1 = 0 0 + s = -4.538722287 + -1 s = -4.538722287 + -1 Combine like terms: -4.538722287 + -1 = -5.538722287 s = -5.538722287 Simplifying s = -5.538722287Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.538722287, -5.538722287}
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