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Simplifying s2 + 20s = -23 Reorder the terms: 20s + s2 = -23 Solving 20s + s2 = -23 Solving for variable 's'. Reorder the terms: 23 + 20s + s2 = -23 + 23 Combine like terms: -23 + 23 = 0 23 + 20s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + 20s + -23 + s2 = 0 + -23 Reorder the terms: 23 + -23 + 20s + s2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 20s + s2 = 0 + -23 20s + s2 = 0 + -23 Combine like terms: 0 + -23 = -23 20s + s2 = -23 The s term is 20s. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20s + 100 + s2 = -23 + 100 Reorder the terms: 100 + 20s + s2 = -23 + 100 Combine like terms: -23 + 100 = 77 100 + 20s + s2 = 77 Factor a perfect square on the left side: (s + 10)(s + 10) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (s + 10) equal to 8.774964387 and -8.774964387.Subproblem 1
s + 10 = 8.774964387 Simplifying s + 10 = 8.774964387 Reorder the terms: 10 + s = 8.774964387 Solving 10 + s = 8.774964387 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + s = 8.774964387 + -10 Combine like terms: 10 + -10 = 0 0 + s = 8.774964387 + -10 s = 8.774964387 + -10 Combine like terms: 8.774964387 + -10 = -1.225035613 s = -1.225035613 Simplifying s = -1.225035613Subproblem 2
s + 10 = -8.774964387 Simplifying s + 10 = -8.774964387 Reorder the terms: 10 + s = -8.774964387 Solving 10 + s = -8.774964387 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + s = -8.774964387 + -10 Combine like terms: 10 + -10 = 0 0 + s = -8.774964387 + -10 s = -8.774964387 + -10 Combine like terms: -8.774964387 + -10 = -18.774964387 s = -18.774964387 Simplifying s = -18.774964387Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.225035613, -18.774964387}
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