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Simplifying 45s2 + -17s + -15 = 0 Reorder the terms: -15 + -17s + 45s2 = 0 Solving -15 + -17s + 45s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.3333333333 + -0.3777777778s + s2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.3777777778s + 0.3333333333 + s2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.3777777778s + s2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.3777777778s + s2 = 0 + 0.3333333333 -0.3777777778s + s2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.3777777778s + s2 = 0.3333333333 The s term is -0.3777777778s. Take half its coefficient (-0.1888888889). Square it (0.03567901235) and add it to both sides. Add '0.03567901235' to each side of the equation. -0.3777777778s + 0.03567901235 + s2 = 0.3333333333 + 0.03567901235 Reorder the terms: 0.03567901235 + -0.3777777778s + s2 = 0.3333333333 + 0.03567901235 Combine like terms: 0.3333333333 + 0.03567901235 = 0.36901234565 0.03567901235 + -0.3777777778s + s2 = 0.36901234565 Factor a perfect square on the left side: (s + -0.1888888889)(s + -0.1888888889) = 0.36901234565 Calculate the square root of the right side: 0.607463864 Break this problem into two subproblems by setting (s + -0.1888888889) equal to 0.607463864 and -0.607463864.Subproblem 1
s + -0.1888888889 = 0.607463864 Simplifying s + -0.1888888889 = 0.607463864 Reorder the terms: -0.1888888889 + s = 0.607463864 Solving -0.1888888889 + s = 0.607463864 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.1888888889' to each side of the equation. -0.1888888889 + 0.1888888889 + s = 0.607463864 + 0.1888888889 Combine like terms: -0.1888888889 + 0.1888888889 = 0.0000000000 0.0000000000 + s = 0.607463864 + 0.1888888889 s = 0.607463864 + 0.1888888889 Combine like terms: 0.607463864 + 0.1888888889 = 0.7963527529 s = 0.7963527529 Simplifying s = 0.7963527529Subproblem 2
s + -0.1888888889 = -0.607463864 Simplifying s + -0.1888888889 = -0.607463864 Reorder the terms: -0.1888888889 + s = -0.607463864 Solving -0.1888888889 + s = -0.607463864 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.1888888889' to each side of the equation. -0.1888888889 + 0.1888888889 + s = -0.607463864 + 0.1888888889 Combine like terms: -0.1888888889 + 0.1888888889 = 0.0000000000 0.0000000000 + s = -0.607463864 + 0.1888888889 s = -0.607463864 + 0.1888888889 Combine like terms: -0.607463864 + 0.1888888889 = -0.4185749751 s = -0.4185749751 Simplifying s = -0.4185749751Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.7963527529, -0.4185749751}
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