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Simplifying 9s2 + 90s + -125 = 0 Reorder the terms: -125 + 90s + 9s2 = 0 Solving -125 + 90s + 9s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -13.88888889 + 10s + s2 = 0 Move the constant term to the right: Add '13.88888889' to each side of the equation. -13.88888889 + 10s + 13.88888889 + s2 = 0 + 13.88888889 Reorder the terms: -13.88888889 + 13.88888889 + 10s + s2 = 0 + 13.88888889 Combine like terms: -13.88888889 + 13.88888889 = 0.00000000 0.00000000 + 10s + s2 = 0 + 13.88888889 10s + s2 = 0 + 13.88888889 Combine like terms: 0 + 13.88888889 = 13.88888889 10s + s2 = 13.88888889 The s term is 10s. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10s + 25 + s2 = 13.88888889 + 25 Reorder the terms: 25 + 10s + s2 = 13.88888889 + 25 Combine like terms: 13.88888889 + 25 = 38.88888889 25 + 10s + s2 = 38.88888889 Factor a perfect square on the left side: (s + 5)(s + 5) = 38.88888889 Calculate the square root of the right side: 6.236095645 Break this problem into two subproblems by setting (s + 5) equal to 6.236095645 and -6.236095645.Subproblem 1
s + 5 = 6.236095645 Simplifying s + 5 = 6.236095645 Reorder the terms: 5 + s = 6.236095645 Solving 5 + s = 6.236095645 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = 6.236095645 + -5 Combine like terms: 5 + -5 = 0 0 + s = 6.236095645 + -5 s = 6.236095645 + -5 Combine like terms: 6.236095645 + -5 = 1.236095645 s = 1.236095645 Simplifying s = 1.236095645Subproblem 2
s + 5 = -6.236095645 Simplifying s + 5 = -6.236095645 Reorder the terms: 5 + s = -6.236095645 Solving 5 + s = -6.236095645 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = -6.236095645 + -5 Combine like terms: 5 + -5 = 0 0 + s = -6.236095645 + -5 s = -6.236095645 + -5 Combine like terms: -6.236095645 + -5 = -11.236095645 s = -11.236095645 Simplifying s = -11.236095645Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.236095645, -11.236095645}
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