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Simplifying (7s2 + 5s) + (-6s2 + -17s + 4) = 0 Reorder the terms: (5s + 7s2) + (-6s2 + -17s + 4) = 0 Remove parenthesis around (5s + 7s2) 5s + 7s2 + (-6s2 + -17s + 4) = 0 Reorder the terms: 5s + 7s2 + (4 + -17s + -6s2) = 0 Remove parenthesis around (4 + -17s + -6s2) 5s + 7s2 + 4 + -17s + -6s2 = 0 Reorder the terms: 4 + 5s + -17s + 7s2 + -6s2 = 0 Combine like terms: 5s + -17s = -12s 4 + -12s + 7s2 + -6s2 = 0 Combine like terms: 7s2 + -6s2 = 1s2 4 + -12s + 1s2 = 0 Solving 4 + -12s + 1s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -12s + -4 + s2 = 0 + -4 Reorder the terms: 4 + -4 + -12s + s2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -12s + s2 = 0 + -4 -12s + s2 = 0 + -4 Combine like terms: 0 + -4 = -4 -12s + s2 = -4 The s term is -12s. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12s + 36 + s2 = -4 + 36 Reorder the terms: 36 + -12s + s2 = -4 + 36 Combine like terms: -4 + 36 = 32 36 + -12s + s2 = 32 Factor a perfect square on the left side: (s + -6)(s + -6) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (s + -6) equal to 5.656854249 and -5.656854249.Subproblem 1
s + -6 = 5.656854249 Simplifying s + -6 = 5.656854249 Reorder the terms: -6 + s = 5.656854249 Solving -6 + s = 5.656854249 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + s = 5.656854249 + 6 Combine like terms: -6 + 6 = 0 0 + s = 5.656854249 + 6 s = 5.656854249 + 6 Combine like terms: 5.656854249 + 6 = 11.656854249 s = 11.656854249 Simplifying s = 11.656854249Subproblem 2
s + -6 = -5.656854249 Simplifying s + -6 = -5.656854249 Reorder the terms: -6 + s = -5.656854249 Solving -6 + s = -5.656854249 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + s = -5.656854249 + 6 Combine like terms: -6 + 6 = 0 0 + s = -5.656854249 + 6 s = -5.656854249 + 6 Combine like terms: -5.656854249 + 6 = 0.343145751 s = 0.343145751 Simplifying s = 0.343145751Solution
The solution to the problem is based on the solutions from the subproblems. s = {11.656854249, 0.343145751}
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