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Simplifying (s + -6)(s + -22) = 72 Reorder the terms: (-6 + s)(s + -22) = 72 Reorder the terms: (-6 + s)(-22 + s) = 72 Multiply (-6 + s) * (-22 + s) (-6(-22 + s) + s(-22 + s)) = 72 ((-22 * -6 + s * -6) + s(-22 + s)) = 72 ((132 + -6s) + s(-22 + s)) = 72 (132 + -6s + (-22 * s + s * s)) = 72 (132 + -6s + (-22s + s2)) = 72 Combine like terms: -6s + -22s = -28s (132 + -28s + s2) = 72 Solving 132 + -28s + s2 = 72 Solving for variable 's'. Reorder the terms: 132 + -72 + -28s + s2 = 72 + -72 Combine like terms: 132 + -72 = 60 60 + -28s + s2 = 72 + -72 Combine like terms: 72 + -72 = 0 60 + -28s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -28s + -60 + s2 = 0 + -60 Reorder the terms: 60 + -60 + -28s + s2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -28s + s2 = 0 + -60 -28s + s2 = 0 + -60 Combine like terms: 0 + -60 = -60 -28s + s2 = -60 The s term is -28s. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28s + 196 + s2 = -60 + 196 Reorder the terms: 196 + -28s + s2 = -60 + 196 Combine like terms: -60 + 196 = 136 196 + -28s + s2 = 136 Factor a perfect square on the left side: (s + -14)(s + -14) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (s + -14) equal to 11.66190379 and -11.66190379.Subproblem 1
s + -14 = 11.66190379 Simplifying s + -14 = 11.66190379 Reorder the terms: -14 + s = 11.66190379 Solving -14 + s = 11.66190379 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + s = 11.66190379 + 14 Combine like terms: -14 + 14 = 0 0 + s = 11.66190379 + 14 s = 11.66190379 + 14 Combine like terms: 11.66190379 + 14 = 25.66190379 s = 25.66190379 Simplifying s = 25.66190379Subproblem 2
s + -14 = -11.66190379 Simplifying s + -14 = -11.66190379 Reorder the terms: -14 + s = -11.66190379 Solving -14 + s = -11.66190379 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + s = -11.66190379 + 14 Combine like terms: -14 + 14 = 0 0 + s = -11.66190379 + 14 s = -11.66190379 + 14 Combine like terms: -11.66190379 + 14 = 2.33809621 s = 2.33809621 Simplifying s = 2.33809621Solution
The solution to the problem is based on the solutions from the subproblems. s = {25.66190379, 2.33809621}
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