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Simplifying s2 + 12s + 12 = 0 Reorder the terms: 12 + 12s + s2 = 0 Solving 12 + 12s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 12s + -12 + s2 = 0 + -12 Reorder the terms: 12 + -12 + 12s + s2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 12s + s2 = 0 + -12 12s + s2 = 0 + -12 Combine like terms: 0 + -12 = -12 12s + s2 = -12 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 = -12 + 36 Reorder the terms: 36 + 12s + s2 = -12 + 36 Combine like terms: -12 + 36 = 24 36 + 12s + s2 = 24 Factor a perfect square on the left side: (s + 6)(s + 6) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (s + 6) equal to 4.898979486 and -4.898979486.Subproblem 1
s + 6 = 4.898979486 Simplifying s + 6 = 4.898979486 Reorder the terms: 6 + s = 4.898979486 Solving 6 + s = 4.898979486 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 = 4.898979486 + -6 Combine like terms: 6 + -6 = 0 0 + s = 4.898979486 + -6 s = 4.898979486 + -6 Combine like terms: 4.898979486 + -6 = -1.101020514 s = -1.101020514 Simplifying s = -1.101020514Subproblem 2
s + 6 = -4.898979486 Simplifying s + 6 = -4.898979486 Reorder the terms: 6 + s = -4.898979486 Solving 6 + s = -4.898979486 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 = -4.898979486 + -6 Combine like terms: 6 + -6 = 0 0 + s = -4.898979486 + -6 s = -4.898979486 + -6 Combine like terms: -4.898979486 + -6 = -10.898979486 s = -10.898979486 Simplifying s = -10.898979486Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.101020514, -10.898979486}
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