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Simplifying 3s2 + -23s + -40 = 0 Reorder the terms: -40 + -23s + 3s2 = 0 Solving -40 + -23s + 3s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.33333333 + -7.666666667s + s2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -7.666666667s + 13.33333333 + s2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -7.666666667s + s2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -7.666666667s + s2 = 0 + 13.33333333 -7.666666667s + s2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -7.666666667s + s2 = 13.33333333 The s term is -7.666666667s. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667s + 14.69444445 + s2 = 13.33333333 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667s + s2 = 13.33333333 + 14.69444445 Combine like terms: 13.33333333 + 14.69444445 = 28.02777778 14.69444445 + -7.666666667s + s2 = 28.02777778 Factor a perfect square on the left side: (s + -3.833333334)(s + -3.833333334) = 28.02777778 Calculate the square root of the right side: 5.294126725 Break this problem into two subproblems by setting (s + -3.833333334) equal to 5.294126725 and -5.294126725.Subproblem 1
s + -3.833333334 = 5.294126725 Simplifying s + -3.833333334 = 5.294126725 Reorder the terms: -3.833333334 + s = 5.294126725 Solving -3.833333334 + s = 5.294126725 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + s = 5.294126725 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + s = 5.294126725 + 3.833333334 s = 5.294126725 + 3.833333334 Combine like terms: 5.294126725 + 3.833333334 = 9.127460059 s = 9.127460059 Simplifying s = 9.127460059Subproblem 2
s + -3.833333334 = -5.294126725 Simplifying s + -3.833333334 = -5.294126725 Reorder the terms: -3.833333334 + s = -5.294126725 Solving -3.833333334 + s = -5.294126725 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + s = -5.294126725 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + s = -5.294126725 + 3.833333334 s = -5.294126725 + 3.833333334 Combine like terms: -5.294126725 + 3.833333334 = -1.460793391 s = -1.460793391 Simplifying s = -1.460793391Solution
The solution to the problem is based on the solutions from the subproblems. s = {9.127460059, -1.460793391}
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