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Simplifying s2 + 9s + 9 = 0 Reorder the terms: 9 + 9s + s2 = 0 Solving 9 + 9s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 9s + -9 + s2 = 0 + -9 Reorder the terms: 9 + -9 + 9s + s2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 9s + s2 = 0 + -9 9s + s2 = 0 + -9 Combine like terms: 0 + -9 = -9 9s + s2 = -9 The s term is 9s. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9s + 20.25 + s2 = -9 + 20.25 Reorder the terms: 20.25 + 9s + s2 = -9 + 20.25 Combine like terms: -9 + 20.25 = 11.25 20.25 + 9s + s2 = 11.25 Factor a perfect square on the left side: (s + 4.5)(s + 4.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (s + 4.5) equal to 3.354101966 and -3.354101966.Subproblem 1
s + 4.5 = 3.354101966 Simplifying s + 4.5 = 3.354101966 Reorder the terms: 4.5 + s = 3.354101966 Solving 4.5 + s = 3.354101966 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + s = 3.354101966 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + s = 3.354101966 + -4.5 s = 3.354101966 + -4.5 Combine like terms: 3.354101966 + -4.5 = -1.145898034 s = -1.145898034 Simplifying s = -1.145898034Subproblem 2
s + 4.5 = -3.354101966 Simplifying s + 4.5 = -3.354101966 Reorder the terms: 4.5 + s = -3.354101966 Solving 4.5 + s = -3.354101966 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + s = -3.354101966 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + s = -3.354101966 + -4.5 s = -3.354101966 + -4.5 Combine like terms: -3.354101966 + -4.5 = -7.854101966 s = -7.854101966 Simplifying s = -7.854101966Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.145898034, -7.854101966}
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