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Simplifying s2 + 12s = 36 Reorder the terms: 12s + s2 = 36 Solving 12s + s2 = 36 Solving for variable 's'. Reorder the terms: -36 + 12s + s2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 12s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 12s + 36 + s2 = 0 + 36 Reorder the terms: -36 + 36 + 12s + s2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 12s + s2 = 0 + 36 12s + s2 = 0 + 36 Combine like terms: 0 + 36 = 36 12s + s2 = 36 The s term is 12s. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12s + 36 + s2 = 36 + 36 Reorder the terms: 36 + 12s + s2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + 12s + s2 = 72 Factor a perfect square on the left side: (s + 6)(s + 6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (s + 6) equal to 8.485281374 and -8.485281374.Subproblem 1
s + 6 = 8.485281374 Simplifying s + 6 = 8.485281374 Reorder the terms: 6 + s = 8.485281374 Solving 6 + s = 8.485281374 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + s = 8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + s = 8.485281374 + -6 s = 8.485281374 + -6 Combine like terms: 8.485281374 + -6 = 2.485281374 s = 2.485281374 Simplifying s = 2.485281374Subproblem 2
s + 6 = -8.485281374 Simplifying s + 6 = -8.485281374 Reorder the terms: 6 + s = -8.485281374 Solving 6 + s = -8.485281374 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + s = -8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + s = -8.485281374 + -6 s = -8.485281374 + -6 Combine like terms: -8.485281374 + -6 = -14.485281374 s = -14.485281374 Simplifying s = -14.485281374Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.485281374, -14.485281374}
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