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Simplifying 49s2 + 28s = 4 Reorder the terms: 28s + 49s2 = 4 Solving 28s + 49s2 = 4 Solving for variable 's'. Reorder the terms: -4 + 28s + 49s2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 28s + 49s2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.08163265306 + 0.5714285714s + s2 = 0 Move the constant term to the right: Add '0.08163265306' to each side of the equation. -0.08163265306 + 0.5714285714s + 0.08163265306 + s2 = 0 + 0.08163265306 Reorder the terms: -0.08163265306 + 0.08163265306 + 0.5714285714s + s2 = 0 + 0.08163265306 Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000 0.00000000000 + 0.5714285714s + s2 = 0 + 0.08163265306 0.5714285714s + s2 = 0 + 0.08163265306 Combine like terms: 0 + 0.08163265306 = 0.08163265306 0.5714285714s + s2 = 0.08163265306 The s term is 0.5714285714s. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714s + 0.08163265305 + s2 = 0.08163265306 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714s + s2 = 0.08163265306 + 0.08163265305 Combine like terms: 0.08163265306 + 0.08163265305 = 0.16326530611 0.08163265305 + 0.5714285714s + s2 = 0.16326530611 Factor a perfect square on the left side: (s + 0.2857142857)(s + 0.2857142857) = 0.16326530611 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (s + 0.2857142857) equal to 0.404061018 and -0.404061018.Subproblem 1
s + 0.2857142857 = 0.404061018 Simplifying s + 0.2857142857 = 0.404061018 Reorder the terms: 0.2857142857 + s = 0.404061018 Solving 0.2857142857 + s = 0.404061018 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + s = 0.404061018 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + s = 0.404061018 + -0.2857142857 s = 0.404061018 + -0.2857142857 Combine like terms: 0.404061018 + -0.2857142857 = 0.1183467323 s = 0.1183467323 Simplifying s = 0.1183467323Subproblem 2
s + 0.2857142857 = -0.404061018 Simplifying s + 0.2857142857 = -0.404061018 Reorder the terms: 0.2857142857 + s = -0.404061018 Solving 0.2857142857 + s = -0.404061018 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + s = -0.404061018 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + s = -0.404061018 + -0.2857142857 s = -0.404061018 + -0.2857142857 Combine like terms: -0.404061018 + -0.2857142857 = -0.6897753037 s = -0.6897753037 Simplifying s = -0.6897753037Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.1183467323, -0.6897753037}
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