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Simplifying -2s(2s + -4) + -8 = -3(4s + 4) + -1 Reorder the terms: -2s(-4 + 2s) + -8 = -3(4s + 4) + -1 (-4 * -2s + 2s * -2s) + -8 = -3(4s + 4) + -1 (8s + -4s2) + -8 = -3(4s + 4) + -1 Reorder the terms: -8 + 8s + -4s2 = -3(4s + 4) + -1 Reorder the terms: -8 + 8s + -4s2 = -3(4 + 4s) + -1 -8 + 8s + -4s2 = (4 * -3 + 4s * -3) + -1 -8 + 8s + -4s2 = (-12 + -12s) + -1 Reorder the terms: -8 + 8s + -4s2 = -12 + -1 + -12s Combine like terms: -12 + -1 = -13 -8 + 8s + -4s2 = -13 + -12s Solving -8 + 8s + -4s2 = -13 + -12s Solving for variable 's'. Reorder the terms: -8 + 13 + 8s + 12s + -4s2 = -13 + -12s + 13 + 12s Combine like terms: -8 + 13 = 5 5 + 8s + 12s + -4s2 = -13 + -12s + 13 + 12s Combine like terms: 8s + 12s = 20s 5 + 20s + -4s2 = -13 + -12s + 13 + 12s Reorder the terms: 5 + 20s + -4s2 = -13 + 13 + -12s + 12s Combine like terms: -13 + 13 = 0 5 + 20s + -4s2 = 0 + -12s + 12s 5 + 20s + -4s2 = -12s + 12s Combine like terms: -12s + 12s = 0 5 + 20s + -4s2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -5s + s2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -5s + 1.25 + s2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -5s + s2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -5s + s2 = 0 + 1.25 -5s + s2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -5s + s2 = 1.25 The s term is -5s. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5s + 6.25 + s2 = 1.25 + 6.25 Reorder the terms: 6.25 + -5s + s2 = 1.25 + 6.25 Combine like terms: 1.25 + 6.25 = 7.5 6.25 + -5s + s2 = 7.5 Factor a perfect square on the left side: (s + -2.5)(s + -2.5) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (s + -2.5) equal to 2.738612788 and -2.738612788.Subproblem 1
s + -2.5 = 2.738612788 Simplifying s + -2.5 = 2.738612788 Reorder the terms: -2.5 + s = 2.738612788 Solving -2.5 + s = 2.738612788 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + s = 2.738612788 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + s = 2.738612788 + 2.5 s = 2.738612788 + 2.5 Combine like terms: 2.738612788 + 2.5 = 5.238612788 s = 5.238612788 Simplifying s = 5.238612788Subproblem 2
s + -2.5 = -2.738612788 Simplifying s + -2.5 = -2.738612788 Reorder the terms: -2.5 + s = -2.738612788 Solving -2.5 + s = -2.738612788 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + s = -2.738612788 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + s = -2.738612788 + 2.5 s = -2.738612788 + 2.5 Combine like terms: -2.738612788 + 2.5 = -0.238612788 s = -0.238612788 Simplifying s = -0.238612788Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.238612788, -0.238612788}
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