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Simplifying 18s2 + -23s + -68 = 0 Reorder the terms: -68 + -23s + 18s2 = 0 Solving -68 + -23s + 18s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -3.777777778 + -1.277777778s + s2 = 0 Move the constant term to the right: Add '3.777777778' to each side of the equation. -3.777777778 + -1.277777778s + 3.777777778 + s2 = 0 + 3.777777778 Reorder the terms: -3.777777778 + 3.777777778 + -1.277777778s + s2 = 0 + 3.777777778 Combine like terms: -3.777777778 + 3.777777778 = 0.000000000 0.000000000 + -1.277777778s + s2 = 0 + 3.777777778 -1.277777778s + s2 = 0 + 3.777777778 Combine like terms: 0 + 3.777777778 = 3.777777778 -1.277777778s + s2 = 3.777777778 The s term is -1.277777778s. Take half its coefficient (-0.638888889). Square it (0.4081790125) and add it to both sides. Add '0.4081790125' to each side of the equation. -1.277777778s + 0.4081790125 + s2 = 3.777777778 + 0.4081790125 Reorder the terms: 0.4081790125 + -1.277777778s + s2 = 3.777777778 + 0.4081790125 Combine like terms: 3.777777778 + 0.4081790125 = 4.1859567905 0.4081790125 + -1.277777778s + s2 = 4.1859567905 Factor a perfect square on the left side: (s + -0.638888889)(s + -0.638888889) = 4.1859567905 Calculate the square root of the right side: 2.045961092 Break this problem into two subproblems by setting (s + -0.638888889) equal to 2.045961092 and -2.045961092.Subproblem 1
s + -0.638888889 = 2.045961092 Simplifying s + -0.638888889 = 2.045961092 Reorder the terms: -0.638888889 + s = 2.045961092 Solving -0.638888889 + s = 2.045961092 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.638888889' to each side of the equation. -0.638888889 + 0.638888889 + s = 2.045961092 + 0.638888889 Combine like terms: -0.638888889 + 0.638888889 = 0.000000000 0.000000000 + s = 2.045961092 + 0.638888889 s = 2.045961092 + 0.638888889 Combine like terms: 2.045961092 + 0.638888889 = 2.684849981 s = 2.684849981 Simplifying s = 2.684849981Subproblem 2
s + -0.638888889 = -2.045961092 Simplifying s + -0.638888889 = -2.045961092 Reorder the terms: -0.638888889 + s = -2.045961092 Solving -0.638888889 + s = -2.045961092 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.638888889' to each side of the equation. -0.638888889 + 0.638888889 + s = -2.045961092 + 0.638888889 Combine like terms: -0.638888889 + 0.638888889 = 0.000000000 0.000000000 + s = -2.045961092 + 0.638888889 s = -2.045961092 + 0.638888889 Combine like terms: -2.045961092 + 0.638888889 = -1.407072203 s = -1.407072203 Simplifying s = -1.407072203Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.684849981, -1.407072203}
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