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Simplifying s2 + 12s + 12 = 8 Reorder the terms: 12 + 12s + s2 = 8 Solving 12 + 12s + s2 = 8 Solving for variable 's'. Reorder the terms: 12 + -8 + 12s + s2 = 8 + -8 Combine like terms: 12 + -8 = 4 4 + 12s + s2 = 8 + -8 Combine like terms: 8 + -8 = 0 4 + 12s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 12s + -4 + s2 = 0 + -4 Reorder the terms: 4 + -4 + 12s + s2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 12s + s2 = 0 + -4 12s + s2 = 0 + -4 Combine like terms: 0 + -4 = -4 12s + s2 = -4 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 = -4 + 36 Reorder the terms: 36 + 12s + s2 = -4 + 36 Combine like terms: -4 + 36 = 32 36 + 12s + s2 = 32 Factor a perfect square on the left side: (s + 6)(s + 6) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (s + 6) equal to 5.656854249 and -5.656854249.Subproblem 1
s + 6 = 5.656854249 Simplifying s + 6 = 5.656854249 Reorder the terms: 6 + s = 5.656854249 Solving 6 + s = 5.656854249 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 = 5.656854249 + -6 Combine like terms: 6 + -6 = 0 0 + s = 5.656854249 + -6 s = 5.656854249 + -6 Combine like terms: 5.656854249 + -6 = -0.343145751 s = -0.343145751 Simplifying s = -0.343145751Subproblem 2
s + 6 = -5.656854249 Simplifying s + 6 = -5.656854249 Reorder the terms: 6 + s = -5.656854249 Solving 6 + s = -5.656854249 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 = -5.656854249 + -6 Combine like terms: 6 + -6 = 0 0 + s = -5.656854249 + -6 s = -5.656854249 + -6 Combine like terms: -5.656854249 + -6 = -11.656854249 s = -11.656854249 Simplifying s = -11.656854249Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.343145751, -11.656854249}
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