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Simplifying s2 + 12s + -15 = 0 Reorder the terms: -15 + 12s + s2 = 0 Solving -15 + 12s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 12s + 15 + s2 = 0 + 15 Reorder the terms: -15 + 15 + 12s + s2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 12s + s2 = 0 + 15 12s + s2 = 0 + 15 Combine like terms: 0 + 15 = 15 12s + s2 = 15 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 = 15 + 36 Reorder the terms: 36 + 12s + s2 = 15 + 36 Combine like terms: 15 + 36 = 51 36 + 12s + s2 = 51 Factor a perfect square on the left side: (s + 6)(s + 6) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (s + 6) equal to 7.141428429 and -7.141428429.Subproblem 1
s + 6 = 7.141428429 Simplifying s + 6 = 7.141428429 Reorder the terms: 6 + s = 7.141428429 Solving 6 + s = 7.141428429 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 = 7.141428429 + -6 Combine like terms: 6 + -6 = 0 0 + s = 7.141428429 + -6 s = 7.141428429 + -6 Combine like terms: 7.141428429 + -6 = 1.141428429 s = 1.141428429 Simplifying s = 1.141428429Subproblem 2
s + 6 = -7.141428429 Simplifying s + 6 = -7.141428429 Reorder the terms: 6 + s = -7.141428429 Solving 6 + s = -7.141428429 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 = -7.141428429 + -6 Combine like terms: 6 + -6 = 0 0 + s = -7.141428429 + -6 s = -7.141428429 + -6 Combine like terms: -7.141428429 + -6 = -13.141428429 s = -13.141428429 Simplifying s = -13.141428429Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.141428429, -13.141428429}
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