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Simplifying s2 + 10s + 5 = 0 Reorder the terms: 5 + 10s + s2 = 0 Solving 5 + 10s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 10s + -5 + s2 = 0 + -5 Reorder the terms: 5 + -5 + 10s + s2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 10s + s2 = 0 + -5 10s + s2 = 0 + -5 Combine like terms: 0 + -5 = -5 10s + s2 = -5 The s term is 10s. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10s + 25 + s2 = -5 + 25 Reorder the terms: 25 + 10s + s2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + 10s + s2 = 20 Factor a perfect square on the left side: (s + 5)(s + 5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (s + 5) equal to 4.472135955 and -4.472135955.Subproblem 1
s + 5 = 4.472135955 Simplifying s + 5 = 4.472135955 Reorder the terms: 5 + s = 4.472135955 Solving 5 + s = 4.472135955 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = 4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + s = 4.472135955 + -5 s = 4.472135955 + -5 Combine like terms: 4.472135955 + -5 = -0.527864045 s = -0.527864045 Simplifying s = -0.527864045Subproblem 2
s + 5 = -4.472135955 Simplifying s + 5 = -4.472135955 Reorder the terms: 5 + s = -4.472135955 Solving 5 + s = -4.472135955 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = -4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + s = -4.472135955 + -5 s = -4.472135955 + -5 Combine like terms: -4.472135955 + -5 = -9.472135955 s = -9.472135955 Simplifying s = -9.472135955Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.527864045, -9.472135955}
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