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Simplifying s2 + 18s = 35 Reorder the terms: 18s + s2 = 35 Solving 18s + s2 = 35 Solving for variable 's'. Reorder the terms: -35 + 18s + s2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 18s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 18s + 35 + s2 = 0 + 35 Reorder the terms: -35 + 35 + 18s + s2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 18s + s2 = 0 + 35 18s + s2 = 0 + 35 Combine like terms: 0 + 35 = 35 18s + s2 = 35 The s term is 18s. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18s + 81 + s2 = 35 + 81 Reorder the terms: 81 + 18s + s2 = 35 + 81 Combine like terms: 35 + 81 = 116 81 + 18s + s2 = 116 Factor a perfect square on the left side: (s + 9)(s + 9) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (s + 9) equal to 10.770329614 and -10.770329614.Subproblem 1
s + 9 = 10.770329614 Simplifying s + 9 = 10.770329614 Reorder the terms: 9 + s = 10.770329614 Solving 9 + s = 10.770329614 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + s = 10.770329614 + -9 Combine like terms: 9 + -9 = 0 0 + s = 10.770329614 + -9 s = 10.770329614 + -9 Combine like terms: 10.770329614 + -9 = 1.770329614 s = 1.770329614 Simplifying s = 1.770329614Subproblem 2
s + 9 = -10.770329614 Simplifying s + 9 = -10.770329614 Reorder the terms: 9 + s = -10.770329614 Solving 9 + s = -10.770329614 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + s = -10.770329614 + -9 Combine like terms: 9 + -9 = 0 0 + s = -10.770329614 + -9 s = -10.770329614 + -9 Combine like terms: -10.770329614 + -9 = -19.770329614 s = -19.770329614 Simplifying s = -19.770329614Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.770329614, -19.770329614}
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