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Simplifying s2 + -28s = -29 Reorder the terms: -28s + s2 = -29 Solving -28s + s2 = -29 Solving for variable 's'. Reorder the terms: 29 + -28s + s2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + -28s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -28s + -29 + s2 = 0 + -29 Reorder the terms: 29 + -29 + -28s + s2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -28s + s2 = 0 + -29 -28s + s2 = 0 + -29 Combine like terms: 0 + -29 = -29 -28s + s2 = -29 The s term is -28s. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28s + 196 + s2 = -29 + 196 Reorder the terms: 196 + -28s + s2 = -29 + 196 Combine like terms: -29 + 196 = 167 196 + -28s + s2 = 167 Factor a perfect square on the left side: (s + -14)(s + -14) = 167 Calculate the square root of the right side: 12.922847983 Break this problem into two subproblems by setting (s + -14) equal to 12.922847983 and -12.922847983.Subproblem 1
s + -14 = 12.922847983 Simplifying s + -14 = 12.922847983 Reorder the terms: -14 + s = 12.922847983 Solving -14 + s = 12.922847983 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + s = 12.922847983 + 14 Combine like terms: -14 + 14 = 0 0 + s = 12.922847983 + 14 s = 12.922847983 + 14 Combine like terms: 12.922847983 + 14 = 26.922847983 s = 26.922847983 Simplifying s = 26.922847983Subproblem 2
s + -14 = -12.922847983 Simplifying s + -14 = -12.922847983 Reorder the terms: -14 + s = -12.922847983 Solving -14 + s = -12.922847983 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + s = -12.922847983 + 14 Combine like terms: -14 + 14 = 0 0 + s = -12.922847983 + 14 s = -12.922847983 + 14 Combine like terms: -12.922847983 + 14 = 1.077152017 s = 1.077152017 Simplifying s = 1.077152017Solution
The solution to the problem is based on the solutions from the subproblems. s = {26.922847983, 1.077152017}
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