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Simplifying s2 + 30s + 11 = 0 Reorder the terms: 11 + 30s + s2 = 0 Solving 11 + 30s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 30s + -11 + s2 = 0 + -11 Reorder the terms: 11 + -11 + 30s + s2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 30s + s2 = 0 + -11 30s + s2 = 0 + -11 Combine like terms: 0 + -11 = -11 30s + s2 = -11 The s term is 30s. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30s + 225 + s2 = -11 + 225 Reorder the terms: 225 + 30s + s2 = -11 + 225 Combine like terms: -11 + 225 = 214 225 + 30s + s2 = 214 Factor a perfect square on the left side: (s + 15)(s + 15) = 214 Calculate the square root of the right side: 14.628738838 Break this problem into two subproblems by setting (s + 15) equal to 14.628738838 and -14.628738838.Subproblem 1
s + 15 = 14.628738838 Simplifying s + 15 = 14.628738838 Reorder the terms: 15 + s = 14.628738838 Solving 15 + s = 14.628738838 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + s = 14.628738838 + -15 Combine like terms: 15 + -15 = 0 0 + s = 14.628738838 + -15 s = 14.628738838 + -15 Combine like terms: 14.628738838 + -15 = -0.371261162 s = -0.371261162 Simplifying s = -0.371261162Subproblem 2
s + 15 = -14.628738838 Simplifying s + 15 = -14.628738838 Reorder the terms: 15 + s = -14.628738838 Solving 15 + s = -14.628738838 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + s = -14.628738838 + -15 Combine like terms: 15 + -15 = 0 0 + s = -14.628738838 + -15 s = -14.628738838 + -15 Combine like terms: -14.628738838 + -15 = -29.628738838 s = -29.628738838 Simplifying s = -29.628738838Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.371261162, -29.628738838}
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