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Simplifying s2 + 20s + -31 = 0 Reorder the terms: -31 + 20s + s2 = 0 Solving -31 + 20s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 20s + 31 + s2 = 0 + 31 Reorder the terms: -31 + 31 + 20s + s2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 20s + s2 = 0 + 31 20s + s2 = 0 + 31 Combine like terms: 0 + 31 = 31 20s + s2 = 31 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 = 31 + 100 Reorder the terms: 100 + 20s + s2 = 31 + 100 Combine like terms: 31 + 100 = 131 100 + 20s + s2 = 131 Factor a perfect square on the left side: (s + 10)(s + 10) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (s + 10) equal to 11.445523142 and -11.445523142.Subproblem 1
s + 10 = 11.445523142 Simplifying s + 10 = 11.445523142 Reorder the terms: 10 + s = 11.445523142 Solving 10 + s = 11.445523142 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 = 11.445523142 + -10 Combine like terms: 10 + -10 = 0 0 + s = 11.445523142 + -10 s = 11.445523142 + -10 Combine like terms: 11.445523142 + -10 = 1.445523142 s = 1.445523142 Simplifying s = 1.445523142Subproblem 2
s + 10 = -11.445523142 Simplifying s + 10 = -11.445523142 Reorder the terms: 10 + s = -11.445523142 Solving 10 + s = -11.445523142 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 = -11.445523142 + -10 Combine like terms: 10 + -10 = 0 0 + s = -11.445523142 + -10 s = -11.445523142 + -10 Combine like terms: -11.445523142 + -10 = -21.445523142 s = -21.445523142 Simplifying s = -21.445523142Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.445523142, -21.445523142}
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