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Simplifying (15s2 + 5s + -13) + (-14s2 + -10s + 8) = 0 Reorder the terms: (-13 + 5s + 15s2) + (-14s2 + -10s + 8) = 0 Remove parenthesis around (-13 + 5s + 15s2) -13 + 5s + 15s2 + (-14s2 + -10s + 8) = 0 Reorder the terms: -13 + 5s + 15s2 + (8 + -10s + -14s2) = 0 Remove parenthesis around (8 + -10s + -14s2) -13 + 5s + 15s2 + 8 + -10s + -14s2 = 0 Reorder the terms: -13 + 8 + 5s + -10s + 15s2 + -14s2 = 0 Combine like terms: -13 + 8 = -5 -5 + 5s + -10s + 15s2 + -14s2 = 0 Combine like terms: 5s + -10s = -5s -5 + -5s + 15s2 + -14s2 = 0 Combine like terms: 15s2 + -14s2 = 1s2 -5 + -5s + 1s2 = 0 Solving -5 + -5s + 1s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -5s + 5 + s2 = 0 + 5 Reorder the terms: -5 + 5 + -5s + s2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5s + s2 = 0 + 5 -5s + s2 = 0 + 5 Combine like terms: 0 + 5 = 5 -5s + s2 = 5 The s term is -5s. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5s + 6.25 + s2 = 5 + 6.25 Reorder the terms: 6.25 + -5s + s2 = 5 + 6.25 Combine like terms: 5 + 6.25 = 11.25 6.25 + -5s + s2 = 11.25 Factor a perfect square on the left side: (s + -2.5)(s + -2.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (s + -2.5) equal to 3.354101966 and -3.354101966.Subproblem 1
s + -2.5 = 3.354101966 Simplifying s + -2.5 = 3.354101966 Reorder the terms: -2.5 + s = 3.354101966 Solving -2.5 + s = 3.354101966 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + s = 3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + s = 3.354101966 + 2.5 s = 3.354101966 + 2.5 Combine like terms: 3.354101966 + 2.5 = 5.854101966 s = 5.854101966 Simplifying s = 5.854101966Subproblem 2
s + -2.5 = -3.354101966 Simplifying s + -2.5 = -3.354101966 Reorder the terms: -2.5 + s = -3.354101966 Solving -2.5 + s = -3.354101966 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + s = -3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + s = -3.354101966 + 2.5 s = -3.354101966 + 2.5 Combine like terms: -3.354101966 + 2.5 = -0.854101966 s = -0.854101966 Simplifying s = -0.854101966Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.854101966, -0.854101966}
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