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Simplifying 3s2 + 20s = 18 Reorder the terms: 20s + 3s2 = 18 Solving 20s + 3s2 = 18 Solving for variable 's'. Reorder the terms: -18 + 20s + 3s2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 20s + 3s2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + 6.666666667s + s2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 6.666666667s + 6 + s2 = 0 + 6 Reorder the terms: -6 + 6 + 6.666666667s + s2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6.666666667s + s2 = 0 + 6 6.666666667s + s2 = 0 + 6 Combine like terms: 0 + 6 = 6 6.666666667s + s2 = 6 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 = 6 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667s + s2 = 6 + 11.11111112 Combine like terms: 6 + 11.11111112 = 17.11111112 11.11111112 + 6.666666667s + s2 = 17.11111112 Factor a perfect square on the left side: (s + 3.333333334)(s + 3.333333334) = 17.11111112 Calculate the square root of the right side: 4.136557883 Break this problem into two subproblems by setting (s + 3.333333334) equal to 4.136557883 and -4.136557883.Subproblem 1
s + 3.333333334 = 4.136557883 Simplifying s + 3.333333334 = 4.136557883 Reorder the terms: 3.333333334 + s = 4.136557883 Solving 3.333333334 + s = 4.136557883 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 = 4.136557883 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + s = 4.136557883 + -3.333333334 s = 4.136557883 + -3.333333334 Combine like terms: 4.136557883 + -3.333333334 = 0.803224549 s = 0.803224549 Simplifying s = 0.803224549Subproblem 2
s + 3.333333334 = -4.136557883 Simplifying s + 3.333333334 = -4.136557883 Reorder the terms: 3.333333334 + s = -4.136557883 Solving 3.333333334 + s = -4.136557883 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 = -4.136557883 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + s = -4.136557883 + -3.333333334 s = -4.136557883 + -3.333333334 Combine like terms: -4.136557883 + -3.333333334 = -7.469891217 s = -7.469891217 Simplifying s = -7.469891217Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.803224549, -7.469891217}
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