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Simplifying s2 + -28s + -41 = 0 Reorder the terms: -41 + -28s + s2 = 0 Solving -41 + -28s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -28s + 41 + s2 = 0 + 41 Reorder the terms: -41 + 41 + -28s + s2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -28s + s2 = 0 + 41 -28s + s2 = 0 + 41 Combine like terms: 0 + 41 = 41 -28s + s2 = 41 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 = 41 + 196 Reorder the terms: 196 + -28s + s2 = 41 + 196 Combine like terms: 41 + 196 = 237 196 + -28s + s2 = 237 Factor a perfect square on the left side: (s + -14)(s + -14) = 237 Calculate the square root of the right side: 15.394804318 Break this problem into two subproblems by setting (s + -14) equal to 15.394804318 and -15.394804318.Subproblem 1
s + -14 = 15.394804318 Simplifying s + -14 = 15.394804318 Reorder the terms: -14 + s = 15.394804318 Solving -14 + s = 15.394804318 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 = 15.394804318 + 14 Combine like terms: -14 + 14 = 0 0 + s = 15.394804318 + 14 s = 15.394804318 + 14 Combine like terms: 15.394804318 + 14 = 29.394804318 s = 29.394804318 Simplifying s = 29.394804318Subproblem 2
s + -14 = -15.394804318 Simplifying s + -14 = -15.394804318 Reorder the terms: -14 + s = -15.394804318 Solving -14 + s = -15.394804318 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 = -15.394804318 + 14 Combine like terms: -14 + 14 = 0 0 + s = -15.394804318 + 14 s = -15.394804318 + 14 Combine like terms: -15.394804318 + 14 = -1.394804318 s = -1.394804318 Simplifying s = -1.394804318Solution
The solution to the problem is based on the solutions from the subproblems. s = {29.394804318, -1.394804318}
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