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Simplifying s2 = 17s + 70 + 0 Reorder the terms: s2 = 70 + 0 + 17s Combine like terms: 70 + 0 = 70 s2 = 70 + 17s Solving s2 = 70 + 17s Solving for variable 's'. Reorder the terms: -70 + -17s + s2 = 70 + 17s + -70 + -17s Reorder the terms: -70 + -17s + s2 = 70 + -70 + 17s + -17s Combine like terms: 70 + -70 = 0 -70 + -17s + s2 = 0 + 17s + -17s -70 + -17s + s2 = 17s + -17s Combine like terms: 17s + -17s = 0 -70 + -17s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -17s + 70 + s2 = 0 + 70 Reorder the terms: -70 + 70 + -17s + s2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -17s + s2 = 0 + 70 -17s + s2 = 0 + 70 Combine like terms: 0 + 70 = 70 -17s + s2 = 70 The s term is -17s. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17s + 72.25 + s2 = 70 + 72.25 Reorder the terms: 72.25 + -17s + s2 = 70 + 72.25 Combine like terms: 70 + 72.25 = 142.25 72.25 + -17s + s2 = 142.25 Factor a perfect square on the left side: (s + -8.5)(s + -8.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (s + -8.5) equal to 11.926860442 and -11.926860442.Subproblem 1
s + -8.5 = 11.926860442 Simplifying s + -8.5 = 11.926860442 Reorder the terms: -8.5 + s = 11.926860442 Solving -8.5 + s = 11.926860442 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + s = 11.926860442 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + s = 11.926860442 + 8.5 s = 11.926860442 + 8.5 Combine like terms: 11.926860442 + 8.5 = 20.426860442 s = 20.426860442 Simplifying s = 20.426860442Subproblem 2
s + -8.5 = -11.926860442 Simplifying s + -8.5 = -11.926860442 Reorder the terms: -8.5 + s = -11.926860442 Solving -8.5 + s = -11.926860442 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + s = -11.926860442 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + s = -11.926860442 + 8.5 s = -11.926860442 + 8.5 Combine like terms: -11.926860442 + 8.5 = -3.426860442 s = -3.426860442 Simplifying s = -3.426860442Solution
The solution to the problem is based on the solutions from the subproblems. s = {20.426860442, -3.426860442}
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