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Simplifying 4s(s + 2) + -6s + 15 = 10 + -1s + 8 Reorder the terms: 4s(2 + s) + -6s + 15 = 10 + -1s + 8 (2 * 4s + s * 4s) + -6s + 15 = 10 + -1s + 8 (8s + 4s2) + -6s + 15 = 10 + -1s + 8 Reorder the terms: 15 + 8s + -6s + 4s2 = 10 + -1s + 8 Combine like terms: 8s + -6s = 2s 15 + 2s + 4s2 = 10 + -1s + 8 Reorder the terms: 15 + 2s + 4s2 = 10 + 8 + -1s Combine like terms: 10 + 8 = 18 15 + 2s + 4s2 = 18 + -1s Solving 15 + 2s + 4s2 = 18 + -1s Solving for variable 's'. Reorder the terms: 15 + -18 + 2s + s + 4s2 = 18 + -1s + -18 + s Combine like terms: 15 + -18 = -3 -3 + 2s + s + 4s2 = 18 + -1s + -18 + s Combine like terms: 2s + s = 3s -3 + 3s + 4s2 = 18 + -1s + -18 + s Reorder the terms: -3 + 3s + 4s2 = 18 + -18 + -1s + s Combine like terms: 18 + -18 = 0 -3 + 3s + 4s2 = 0 + -1s + s -3 + 3s + 4s2 = -1s + s Combine like terms: -1s + s = 0 -3 + 3s + 4s2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 0.75s + s2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.75s + 0.75 + s2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.75s + s2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.75s + s2 = 0 + 0.75 0.75s + s2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.75s + s2 = 0.75 The s term is 0.75s. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75s + 0.140625 + s2 = 0.75 + 0.140625 Reorder the terms: 0.140625 + 0.75s + s2 = 0.75 + 0.140625 Combine like terms: 0.75 + 0.140625 = 0.890625 0.140625 + 0.75s + s2 = 0.890625 Factor a perfect square on the left side: (s + 0.375)(s + 0.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (s + 0.375) equal to 0.943729304 and -0.943729304.Subproblem 1
s + 0.375 = 0.943729304 Simplifying s + 0.375 = 0.943729304 Reorder the terms: 0.375 + s = 0.943729304 Solving 0.375 + s = 0.943729304 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + s = 0.943729304 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + s = 0.943729304 + -0.375 s = 0.943729304 + -0.375 Combine like terms: 0.943729304 + -0.375 = 0.568729304 s = 0.568729304 Simplifying s = 0.568729304Subproblem 2
s + 0.375 = -0.943729304 Simplifying s + 0.375 = -0.943729304 Reorder the terms: 0.375 + s = -0.943729304 Solving 0.375 + s = -0.943729304 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + s = -0.943729304 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + s = -0.943729304 + -0.375 s = -0.943729304 + -0.375 Combine like terms: -0.943729304 + -0.375 = -1.318729304 s = -1.318729304 Simplifying s = -1.318729304Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.568729304, -1.318729304}
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