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Simplifying s2 = 45 + -4s + -1s2 Solving s2 = 45 + -4s + -1s2 Solving for variable 's'. Reorder the terms: -45 + 4s + s2 + s2 = 45 + -4s + -1s2 + -45 + 4s + s2 Combine like terms: s2 + s2 = 2s2 -45 + 4s + 2s2 = 45 + -4s + -1s2 + -45 + 4s + s2 Reorder the terms: -45 + 4s + 2s2 = 45 + -45 + -4s + 4s + -1s2 + s2 Combine like terms: 45 + -45 = 0 -45 + 4s + 2s2 = 0 + -4s + 4s + -1s2 + s2 -45 + 4s + 2s2 = -4s + 4s + -1s2 + s2 Combine like terms: -4s + 4s = 0 -45 + 4s + 2s2 = 0 + -1s2 + s2 -45 + 4s + 2s2 = -1s2 + s2 Combine like terms: -1s2 + s2 = 0 -45 + 4s + 2s2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + 2s + s2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 2s + 22.5 + s2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 2s + s2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 2s + s2 = 0 + 22.5 2s + s2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 2s + s2 = 22.5 The s term is 2s. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2s + 1 + s2 = 22.5 + 1 Reorder the terms: 1 + 2s + s2 = 22.5 + 1 Combine like terms: 22.5 + 1 = 23.5 1 + 2s + s2 = 23.5 Factor a perfect square on the left side: (s + 1)(s + 1) = 23.5 Calculate the square root of the right side: 4.847679857 Break this problem into two subproblems by setting (s + 1) equal to 4.847679857 and -4.847679857.Subproblem 1
s + 1 = 4.847679857 Simplifying s + 1 = 4.847679857 Reorder the terms: 1 + s = 4.847679857 Solving 1 + s = 4.847679857 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = 4.847679857 + -1 Combine like terms: 1 + -1 = 0 0 + s = 4.847679857 + -1 s = 4.847679857 + -1 Combine like terms: 4.847679857 + -1 = 3.847679857 s = 3.847679857 Simplifying s = 3.847679857Subproblem 2
s + 1 = -4.847679857 Simplifying s + 1 = -4.847679857 Reorder the terms: 1 + s = -4.847679857 Solving 1 + s = -4.847679857 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = -4.847679857 + -1 Combine like terms: 1 + -1 = 0 0 + s = -4.847679857 + -1 s = -4.847679857 + -1 Combine like terms: -4.847679857 + -1 = -5.847679857 s = -5.847679857 Simplifying s = -5.847679857Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.847679857, -5.847679857}
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