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Simplifying s2 + 12s + 18 = 0 Reorder the terms: 18 + 12s + s2 = 0 Solving 18 + 12s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 12s + -18 + s2 = 0 + -18 Reorder the terms: 18 + -18 + 12s + s2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 12s + s2 = 0 + -18 12s + s2 = 0 + -18 Combine like terms: 0 + -18 = -18 12s + s2 = -18 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 = -18 + 36 Reorder the terms: 36 + 12s + s2 = -18 + 36 Combine like terms: -18 + 36 = 18 36 + 12s + s2 = 18 Factor a perfect square on the left side: (s + 6)(s + 6) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (s + 6) equal to 4.242640687 and -4.242640687.Subproblem 1
s + 6 = 4.242640687 Simplifying s + 6 = 4.242640687 Reorder the terms: 6 + s = 4.242640687 Solving 6 + s = 4.242640687 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 = 4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + s = 4.242640687 + -6 s = 4.242640687 + -6 Combine like terms: 4.242640687 + -6 = -1.757359313 s = -1.757359313 Simplifying s = -1.757359313Subproblem 2
s + 6 = -4.242640687 Simplifying s + 6 = -4.242640687 Reorder the terms: 6 + s = -4.242640687 Solving 6 + s = -4.242640687 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 = -4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + s = -4.242640687 + -6 s = -4.242640687 + -6 Combine like terms: -4.242640687 + -6 = -10.242640687 s = -10.242640687 Simplifying s = -10.242640687Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.757359313, -10.242640687}
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