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Simplifying -4s2 + -100s = 168 Reorder the terms: -100s + -4s2 = 168 Solving -100s + -4s2 = 168 Solving for variable 's'. Reorder the terms: -168 + -100s + -4s2 = 168 + -168 Combine like terms: 168 + -168 = 0 -168 + -100s + -4s2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(42 + 25s + s2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(42 + 25s + s2)' equal to zero and attempt to solve: Simplifying 42 + 25s + s2 = 0 Solving 42 + 25s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + 25s + -42 + s2 = 0 + -42 Reorder the terms: 42 + -42 + 25s + s2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 25s + s2 = 0 + -42 25s + s2 = 0 + -42 Combine like terms: 0 + -42 = -42 25s + s2 = -42 The s term is 25s. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25s + 156.25 + s2 = -42 + 156.25 Reorder the terms: 156.25 + 25s + s2 = -42 + 156.25 Combine like terms: -42 + 156.25 = 114.25 156.25 + 25s + s2 = 114.25 Factor a perfect square on the left side: (s + 12.5)(s + 12.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (s + 12.5) equal to 10.688779163 and -10.688779163.Subproblem 1
s + 12.5 = 10.688779163 Simplifying s + 12.5 = 10.688779163 Reorder the terms: 12.5 + s = 10.688779163 Solving 12.5 + s = 10.688779163 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + s = 10.688779163 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + s = 10.688779163 + -12.5 s = 10.688779163 + -12.5 Combine like terms: 10.688779163 + -12.5 = -1.811220837 s = -1.811220837 Simplifying s = -1.811220837Subproblem 2
s + 12.5 = -10.688779163 Simplifying s + 12.5 = -10.688779163 Reorder the terms: 12.5 + s = -10.688779163 Solving 12.5 + s = -10.688779163 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + s = -10.688779163 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + s = -10.688779163 + -12.5 s = -10.688779163 + -12.5 Combine like terms: -10.688779163 + -12.5 = -23.188779163 s = -23.188779163 Simplifying s = -23.188779163Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.811220837, -23.188779163}Solution
s = {-1.811220837, -23.188779163}
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