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Simplifying (2s + 2)(s + 4) = 192 Reorder the terms: (2 + 2s)(s + 4) = 192 Reorder the terms: (2 + 2s)(4 + s) = 192 Multiply (2 + 2s) * (4 + s) (2(4 + s) + 2s * (4 + s)) = 192 ((4 * 2 + s * 2) + 2s * (4 + s)) = 192 ((8 + 2s) + 2s * (4 + s)) = 192 (8 + 2s + (4 * 2s + s * 2s)) = 192 (8 + 2s + (8s + 2s2)) = 192 Combine like terms: 2s + 8s = 10s (8 + 10s + 2s2) = 192 Solving 8 + 10s + 2s2 = 192 Solving for variable 's'. Reorder the terms: 8 + -192 + 10s + 2s2 = 192 + -192 Combine like terms: 8 + -192 = -184 -184 + 10s + 2s2 = 192 + -192 Combine like terms: 192 + -192 = 0 -184 + 10s + 2s2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-92 + 5s + s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-92 + 5s + s2)' equal to zero and attempt to solve: Simplifying -92 + 5s + s2 = 0 Solving -92 + 5s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 5s + 92 + s2 = 0 + 92 Reorder the terms: -92 + 92 + 5s + s2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 5s + s2 = 0 + 92 5s + s2 = 0 + 92 Combine like terms: 0 + 92 = 92 5s + s2 = 92 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 = 92 + 6.25 Reorder the terms: 6.25 + 5s + s2 = 92 + 6.25 Combine like terms: 92 + 6.25 = 98.25 6.25 + 5s + s2 = 98.25 Factor a perfect square on the left side: (s + 2.5)(s + 2.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (s + 2.5) equal to 9.912113801 and -9.912113801.Subproblem 1
s + 2.5 = 9.912113801 Simplifying s + 2.5 = 9.912113801 Reorder the terms: 2.5 + s = 9.912113801 Solving 2.5 + s = 9.912113801 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 = 9.912113801 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = 9.912113801 + -2.5 s = 9.912113801 + -2.5 Combine like terms: 9.912113801 + -2.5 = 7.412113801 s = 7.412113801 Simplifying s = 7.412113801Subproblem 2
s + 2.5 = -9.912113801 Simplifying s + 2.5 = -9.912113801 Reorder the terms: 2.5 + s = -9.912113801 Solving 2.5 + s = -9.912113801 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 = -9.912113801 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = -9.912113801 + -2.5 s = -9.912113801 + -2.5 Combine like terms: -9.912113801 + -2.5 = -12.412113801 s = -12.412113801 Simplifying s = -12.412113801Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.412113801, -12.412113801}Solution
s = {7.412113801, -12.412113801}
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