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Simplifying s2 + 24s = 35 Reorder the terms: 24s + s2 = 35 Solving 24s + s2 = 35 Solving for variable 's'. Reorder the terms: -35 + 24s + s2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 24s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 24s + 35 + s2 = 0 + 35 Reorder the terms: -35 + 35 + 24s + s2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 24s + s2 = 0 + 35 24s + s2 = 0 + 35 Combine like terms: 0 + 35 = 35 24s + s2 = 35 The s term is 24s. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24s + 144 + s2 = 35 + 144 Reorder the terms: 144 + 24s + s2 = 35 + 144 Combine like terms: 35 + 144 = 179 144 + 24s + s2 = 179 Factor a perfect square on the left side: (s + 12)(s + 12) = 179 Calculate the square root of the right side: 13.37908816 Break this problem into two subproblems by setting (s + 12) equal to 13.37908816 and -13.37908816.Subproblem 1
s + 12 = 13.37908816 Simplifying s + 12 = 13.37908816 Reorder the terms: 12 + s = 13.37908816 Solving 12 + s = 13.37908816 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + s = 13.37908816 + -12 Combine like terms: 12 + -12 = 0 0 + s = 13.37908816 + -12 s = 13.37908816 + -12 Combine like terms: 13.37908816 + -12 = 1.37908816 s = 1.37908816 Simplifying s = 1.37908816Subproblem 2
s + 12 = -13.37908816 Simplifying s + 12 = -13.37908816 Reorder the terms: 12 + s = -13.37908816 Solving 12 + s = -13.37908816 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + s = -13.37908816 + -12 Combine like terms: 12 + -12 = 0 0 + s = -13.37908816 + -12 s = -13.37908816 + -12 Combine like terms: -13.37908816 + -12 = -25.37908816 s = -25.37908816 Simplifying s = -25.37908816Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.37908816, -25.37908816}
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