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Simplifying -6s2 + 24s + -1 = 0 Reorder the terms: -1 + 24s + -6s2 = 0 Solving -1 + 24s + -6s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.1666666667 + -4s + s2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -4s + -0.1666666667 + s2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -4s + s2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -4s + s2 = 0 + -0.1666666667 -4s + s2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -4s + s2 = -0.1666666667 The s term is -4s. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4s + 4 + s2 = -0.1666666667 + 4 Reorder the terms: 4 + -4s + s2 = -0.1666666667 + 4 Combine like terms: -0.1666666667 + 4 = 3.8333333333 4 + -4s + s2 = 3.8333333333 Factor a perfect square on the left side: (s + -2)(s + -2) = 3.8333333333 Calculate the square root of the right side: 1.957890021 Break this problem into two subproblems by setting (s + -2) equal to 1.957890021 and -1.957890021.Subproblem 1
s + -2 = 1.957890021 Simplifying s + -2 = 1.957890021 Reorder the terms: -2 + s = 1.957890021 Solving -2 + s = 1.957890021 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + s = 1.957890021 + 2 Combine like terms: -2 + 2 = 0 0 + s = 1.957890021 + 2 s = 1.957890021 + 2 Combine like terms: 1.957890021 + 2 = 3.957890021 s = 3.957890021 Simplifying s = 3.957890021Subproblem 2
s + -2 = -1.957890021 Simplifying s + -2 = -1.957890021 Reorder the terms: -2 + s = -1.957890021 Solving -2 + s = -1.957890021 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + s = -1.957890021 + 2 Combine like terms: -2 + 2 = 0 0 + s = -1.957890021 + 2 s = -1.957890021 + 2 Combine like terms: -1.957890021 + 2 = 0.042109979 s = 0.042109979 Simplifying s = 0.042109979Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.957890021, 0.042109979}
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