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Simplifying 8s2 + -5s + -1 = 0 Reorder the terms: -1 + -5s + 8s2 = 0 Solving -1 + -5s + 8s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.625s + s2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.625s + 0.125 + s2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.625s + s2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.625s + s2 = 0 + 0.125 -0.625s + s2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.625s + s2 = 0.125 The s term is -0.625s. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625s + 0.09765625 + s2 = 0.125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625s + s2 = 0.125 + 0.09765625 Combine like terms: 0.125 + 0.09765625 = 0.22265625 0.09765625 + -0.625s + s2 = 0.22265625 Factor a perfect square on the left side: (s + -0.3125)(s + -0.3125) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (s + -0.3125) equal to 0.471864652 and -0.471864652.Subproblem 1
s + -0.3125 = 0.471864652 Simplifying s + -0.3125 = 0.471864652 Reorder the terms: -0.3125 + s = 0.471864652 Solving -0.3125 + s = 0.471864652 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + s = 0.471864652 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + s = 0.471864652 + 0.3125 s = 0.471864652 + 0.3125 Combine like terms: 0.471864652 + 0.3125 = 0.784364652 s = 0.784364652 Simplifying s = 0.784364652Subproblem 2
s + -0.3125 = -0.471864652 Simplifying s + -0.3125 = -0.471864652 Reorder the terms: -0.3125 + s = -0.471864652 Solving -0.3125 + s = -0.471864652 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + s = -0.471864652 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + s = -0.471864652 + 0.3125 s = -0.471864652 + 0.3125 Combine like terms: -0.471864652 + 0.3125 = -0.159364652 s = -0.159364652 Simplifying s = -0.159364652Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.784364652, -0.159364652}
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