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Simplifying 20 + -39s = 18s2 Solving 20 + -39s = 18s2 Solving for variable 's'. Combine like terms: 18s2 + -18s2 = 0 20 + -39s + -18s2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -1.111111111 + 2.166666667s + s2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 2.166666667s + 1.111111111 + s2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 2.166666667s + s2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 2.166666667s + s2 = 0 + 1.111111111 2.166666667s + s2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 2.166666667s + s2 = 1.111111111 The s term is 2.166666667s. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667s + 1.173611113 + s2 = 1.111111111 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667s + s2 = 1.111111111 + 1.173611113 Combine like terms: 1.111111111 + 1.173611113 = 2.284722224 1.173611113 + 2.166666667s + s2 = 2.284722224 Factor a perfect square on the left side: (s + 1.083333334)(s + 1.083333334) = 2.284722224 Calculate the square root of the right side: 1.511529763 Break this problem into two subproblems by setting (s + 1.083333334) equal to 1.511529763 and -1.511529763.Subproblem 1
s + 1.083333334 = 1.511529763 Simplifying s + 1.083333334 = 1.511529763 Reorder the terms: 1.083333334 + s = 1.511529763 Solving 1.083333334 + s = 1.511529763 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + s = 1.511529763 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + s = 1.511529763 + -1.083333334 s = 1.511529763 + -1.083333334 Combine like terms: 1.511529763 + -1.083333334 = 0.428196429 s = 0.428196429 Simplifying s = 0.428196429Subproblem 2
s + 1.083333334 = -1.511529763 Simplifying s + 1.083333334 = -1.511529763 Reorder the terms: 1.083333334 + s = -1.511529763 Solving 1.083333334 + s = -1.511529763 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + s = -1.511529763 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + s = -1.511529763 + -1.083333334 s = -1.511529763 + -1.083333334 Combine like terms: -1.511529763 + -1.083333334 = -2.594863097 s = -2.594863097 Simplifying s = -2.594863097Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.428196429, -2.594863097}
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