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Simplifying s2 + 12s + -12 = 14 Reorder the terms: -12 + 12s + s2 = 14 Solving -12 + 12s + s2 = 14 Solving for variable 's'. Reorder the terms: -12 + -14 + 12s + s2 = 14 + -14 Combine like terms: -12 + -14 = -26 -26 + 12s + s2 = 14 + -14 Combine like terms: 14 + -14 = 0 -26 + 12s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 12s + 26 + s2 = 0 + 26 Reorder the terms: -26 + 26 + 12s + s2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 12s + s2 = 0 + 26 12s + s2 = 0 + 26 Combine like terms: 0 + 26 = 26 12s + s2 = 26 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 = 26 + 36 Reorder the terms: 36 + 12s + s2 = 26 + 36 Combine like terms: 26 + 36 = 62 36 + 12s + s2 = 62 Factor a perfect square on the left side: (s + 6)(s + 6) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (s + 6) equal to 7.874007874 and -7.874007874.Subproblem 1
s + 6 = 7.874007874 Simplifying s + 6 = 7.874007874 Reorder the terms: 6 + s = 7.874007874 Solving 6 + s = 7.874007874 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 = 7.874007874 + -6 Combine like terms: 6 + -6 = 0 0 + s = 7.874007874 + -6 s = 7.874007874 + -6 Combine like terms: 7.874007874 + -6 = 1.874007874 s = 1.874007874 Simplifying s = 1.874007874Subproblem 2
s + 6 = -7.874007874 Simplifying s + 6 = -7.874007874 Reorder the terms: 6 + s = -7.874007874 Solving 6 + s = -7.874007874 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 = -7.874007874 + -6 Combine like terms: 6 + -6 = 0 0 + s = -7.874007874 + -6 s = -7.874007874 + -6 Combine like terms: -7.874007874 + -6 = -13.874007874 s = -13.874007874 Simplifying s = -13.874007874Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.874007874, -13.874007874}
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