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Simplifying s2 + 19s + 20 = 0 Reorder the terms: 20 + 19s + s2 = 0 Solving 20 + 19s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 19s + -20 + s2 = 0 + -20 Reorder the terms: 20 + -20 + 19s + s2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 19s + s2 = 0 + -20 19s + s2 = 0 + -20 Combine like terms: 0 + -20 = -20 19s + s2 = -20 The s term is 19s. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19s + 90.25 + s2 = -20 + 90.25 Reorder the terms: 90.25 + 19s + s2 = -20 + 90.25 Combine like terms: -20 + 90.25 = 70.25 90.25 + 19s + s2 = 70.25 Factor a perfect square on the left side: (s + 9.5)(s + 9.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (s + 9.5) equal to 8.381527307 and -8.381527307.Subproblem 1
s + 9.5 = 8.381527307 Simplifying s + 9.5 = 8.381527307 Reorder the terms: 9.5 + s = 8.381527307 Solving 9.5 + s = 8.381527307 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + s = 8.381527307 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + s = 8.381527307 + -9.5 s = 8.381527307 + -9.5 Combine like terms: 8.381527307 + -9.5 = -1.118472693 s = -1.118472693 Simplifying s = -1.118472693Subproblem 2
s + 9.5 = -8.381527307 Simplifying s + 9.5 = -8.381527307 Reorder the terms: 9.5 + s = -8.381527307 Solving 9.5 + s = -8.381527307 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + s = -8.381527307 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + s = -8.381527307 + -9.5 s = -8.381527307 + -9.5 Combine like terms: -8.381527307 + -9.5 = -17.881527307 s = -17.881527307 Simplifying s = -17.881527307Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.118472693, -17.881527307}
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