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Simplifying s2 + 5s = 15 Reorder the terms: 5s + s2 = 15 Solving 5s + s2 = 15 Solving for variable 's'. Reorder the terms: -15 + 5s + s2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 5s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 5s + 15 + s2 = 0 + 15 Reorder the terms: -15 + 15 + 5s + s2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 5s + s2 = 0 + 15 5s + s2 = 0 + 15 Combine like terms: 0 + 15 = 15 5s + s2 = 15 The s term is 5s. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5s + 6.25 + s2 = 15 + 6.25 Reorder the terms: 6.25 + 5s + s2 = 15 + 6.25 Combine like terms: 15 + 6.25 = 21.25 6.25 + 5s + s2 = 21.25 Factor a perfect square on the left side: (s + 2.5)(s + 2.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (s + 2.5) equal to 4.609772229 and -4.609772229.Subproblem 1
s + 2.5 = 4.609772229 Simplifying s + 2.5 = 4.609772229 Reorder the terms: 2.5 + s = 4.609772229 Solving 2.5 + s = 4.609772229 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + s = 4.609772229 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = 4.609772229 + -2.5 s = 4.609772229 + -2.5 Combine like terms: 4.609772229 + -2.5 = 2.109772229 s = 2.109772229 Simplifying s = 2.109772229Subproblem 2
s + 2.5 = -4.609772229 Simplifying s + 2.5 = -4.609772229 Reorder the terms: 2.5 + s = -4.609772229 Solving 2.5 + s = -4.609772229 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + s = -4.609772229 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = -4.609772229 + -2.5 s = -4.609772229 + -2.5 Combine like terms: -4.609772229 + -2.5 = -7.109772229 s = -7.109772229 Simplifying s = -7.109772229Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.109772229, -7.109772229}
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