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Simplifying s2 + 18s + 15 = 0 Reorder the terms: 15 + 18s + s2 = 0 Solving 15 + 18s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 18s + -15 + s2 = 0 + -15 Reorder the terms: 15 + -15 + 18s + s2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 18s + s2 = 0 + -15 18s + s2 = 0 + -15 Combine like terms: 0 + -15 = -15 18s + s2 = -15 The s term is 18s. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18s + 81 + s2 = -15 + 81 Reorder the terms: 81 + 18s + s2 = -15 + 81 Combine like terms: -15 + 81 = 66 81 + 18s + s2 = 66 Factor a perfect square on the left side: (s + 9)(s + 9) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (s + 9) equal to 8.124038405 and -8.124038405.Subproblem 1
s + 9 = 8.124038405 Simplifying s + 9 = 8.124038405 Reorder the terms: 9 + s = 8.124038405 Solving 9 + s = 8.124038405 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + s = 8.124038405 + -9 Combine like terms: 9 + -9 = 0 0 + s = 8.124038405 + -9 s = 8.124038405 + -9 Combine like terms: 8.124038405 + -9 = -0.875961595 s = -0.875961595 Simplifying s = -0.875961595Subproblem 2
s + 9 = -8.124038405 Simplifying s + 9 = -8.124038405 Reorder the terms: 9 + s = -8.124038405 Solving 9 + s = -8.124038405 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + s = -8.124038405 + -9 Combine like terms: 9 + -9 = 0 0 + s = -8.124038405 + -9 s = -8.124038405 + -9 Combine like terms: -8.124038405 + -9 = -17.124038405 s = -17.124038405 Simplifying s = -17.124038405Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.875961595, -17.124038405}
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