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Simplifying s2 = 16 + -16s Solving s2 = 16 + -16s Solving for variable 's'. Reorder the terms: -16 + 16s + s2 = 16 + -16s + -16 + 16s Reorder the terms: -16 + 16s + s2 = 16 + -16 + -16s + 16s Combine like terms: 16 + -16 = 0 -16 + 16s + s2 = 0 + -16s + 16s -16 + 16s + s2 = -16s + 16s Combine like terms: -16s + 16s = 0 -16 + 16s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 16s + 16 + s2 = 0 + 16 Reorder the terms: -16 + 16 + 16s + s2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 16s + s2 = 0 + 16 16s + s2 = 0 + 16 Combine like terms: 0 + 16 = 16 16s + s2 = 16 The s term is 16s. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16s + 64 + s2 = 16 + 64 Reorder the terms: 64 + 16s + s2 = 16 + 64 Combine like terms: 16 + 64 = 80 64 + 16s + s2 = 80 Factor a perfect square on the left side: (s + 8)(s + 8) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (s + 8) equal to 8.94427191 and -8.94427191.Subproblem 1
s + 8 = 8.94427191 Simplifying s + 8 = 8.94427191 Reorder the terms: 8 + s = 8.94427191 Solving 8 + s = 8.94427191 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + s = 8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + s = 8.94427191 + -8 s = 8.94427191 + -8 Combine like terms: 8.94427191 + -8 = 0.94427191 s = 0.94427191 Simplifying s = 0.94427191Subproblem 2
s + 8 = -8.94427191 Simplifying s + 8 = -8.94427191 Reorder the terms: 8 + s = -8.94427191 Solving 8 + s = -8.94427191 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + s = -8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + s = -8.94427191 + -8 s = -8.94427191 + -8 Combine like terms: -8.94427191 + -8 = -16.94427191 s = -16.94427191 Simplifying s = -16.94427191Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.94427191, -16.94427191}
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