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Simplifying s = 12 + -0.25s2 Solving s = 12 + -0.25s2 Solving for variable 's'. Reorder the terms: -12 + s + 0.25s2 = 12 + -0.25s2 + -12 + 0.25s2 Reorder the terms: -12 + s + 0.25s2 = 12 + -12 + -0.25s2 + 0.25s2 Combine like terms: 12 + -12 = 0 -12 + s + 0.25s2 = 0 + -0.25s2 + 0.25s2 -12 + s + 0.25s2 = -0.25s2 + 0.25s2 Combine like terms: -0.25s2 + 0.25s2 = 0.00 -12 + s + 0.25s2 = 0.00 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -48 + 4s + s2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 4s + 48 + s2 = 0 + 48 Reorder the terms: -48 + 48 + 4s + s2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 4s + s2 = 0 + 48 4s + s2 = 0 + 48 Combine like terms: 0 + 48 = 48 4s + s2 = 48 The s term is s. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 4s + 0.25 + s2 = 48 + 0.25 Reorder the terms: 0.25 + 4s + s2 = 48 + 0.25 Combine like terms: 48 + 0.25 = 48.25 0.25 + 4s + s2 = 48.25 Factor a perfect square on the left side: (s + 0.5)(s + 0.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (s + 0.5) equal to 6.946221995 and -6.946221995.Subproblem 1
s + 0.5 = 6.946221995 Simplifying s + 0.5 = 6.946221995 Reorder the terms: 0.5 + s = 6.946221995 Solving 0.5 + s = 6.946221995 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + s = 6.946221995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + s = 6.946221995 + -0.5 s = 6.946221995 + -0.5 Combine like terms: 6.946221995 + -0.5 = 6.446221995 s = 6.446221995 Simplifying s = 6.446221995Subproblem 2
s + 0.5 = -6.946221995 Simplifying s + 0.5 = -6.946221995 Reorder the terms: 0.5 + s = -6.946221995 Solving 0.5 + s = -6.946221995 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + s = -6.946221995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + s = -6.946221995 + -0.5 s = -6.946221995 + -0.5 Combine like terms: -6.946221995 + -0.5 = -7.446221995 s = -7.446221995 Simplifying s = -7.446221995Solution
The solution to the problem is based on the solutions from the subproblems. s = {6.446221995, -7.446221995}
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