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Simplifying 3s2 + 20s = 180 Reorder the terms: 20s + 3s2 = 180 Solving 20s + 3s2 = 180 Solving for variable 's'. Reorder the terms: -180 + 20s + 3s2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 20s + 3s2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -60 + 6.666666667s + s2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 6.666666667s + 60 + s2 = 0 + 60 Reorder the terms: -60 + 60 + 6.666666667s + s2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 6.666666667s + s2 = 0 + 60 6.666666667s + s2 = 0 + 60 Combine like terms: 0 + 60 = 60 6.666666667s + s2 = 60 The s term is 6.666666667s. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667s + 11.11111112 + s2 = 60 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667s + s2 = 60 + 11.11111112 Combine like terms: 60 + 11.11111112 = 71.11111112 11.11111112 + 6.666666667s + s2 = 71.11111112 Factor a perfect square on the left side: (s + 3.333333334)(s + 3.333333334) = 71.11111112 Calculate the square root of the right side: 8.432740428 Break this problem into two subproblems by setting (s + 3.333333334) equal to 8.432740428 and -8.432740428.Subproblem 1
s + 3.333333334 = 8.432740428 Simplifying s + 3.333333334 = 8.432740428 Reorder the terms: 3.333333334 + s = 8.432740428 Solving 3.333333334 + s = 8.432740428 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + s = 8.432740428 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + s = 8.432740428 + -3.333333334 s = 8.432740428 + -3.333333334 Combine like terms: 8.432740428 + -3.333333334 = 5.099407094 s = 5.099407094 Simplifying s = 5.099407094Subproblem 2
s + 3.333333334 = -8.432740428 Simplifying s + 3.333333334 = -8.432740428 Reorder the terms: 3.333333334 + s = -8.432740428 Solving 3.333333334 + s = -8.432740428 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + s = -8.432740428 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + s = -8.432740428 + -3.333333334 s = -8.432740428 + -3.333333334 Combine like terms: -8.432740428 + -3.333333334 = -11.766073762 s = -11.766073762 Simplifying s = -11.766073762Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.099407094, -11.766073762}
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