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Simplifying 140s + 4s2 + -81120 = 0 Reorder the terms: -81120 + 140s + 4s2 = 0 Solving -81120 + 140s + 4s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '4'. 4(-20280 + 35s + s2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-20280 + 35s + s2)' equal to zero and attempt to solve: Simplifying -20280 + 35s + s2 = 0 Solving -20280 + 35s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '20280' to each side of the equation. -20280 + 35s + 20280 + s2 = 0 + 20280 Reorder the terms: -20280 + 20280 + 35s + s2 = 0 + 20280 Combine like terms: -20280 + 20280 = 0 0 + 35s + s2 = 0 + 20280 35s + s2 = 0 + 20280 Combine like terms: 0 + 20280 = 20280 35s + s2 = 20280 The s term is 35s. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35s + 306.25 + s2 = 20280 + 306.25 Reorder the terms: 306.25 + 35s + s2 = 20280 + 306.25 Combine like terms: 20280 + 306.25 = 20586.25 306.25 + 35s + s2 = 20586.25 Factor a perfect square on the left side: (s + 17.5)(s + 17.5) = 20586.25 Calculate the square root of the right side: 143.479092554 Break this problem into two subproblems by setting (s + 17.5) equal to 143.479092554 and -143.479092554.Subproblem 1
s + 17.5 = 143.479092554 Simplifying s + 17.5 = 143.479092554 Reorder the terms: 17.5 + s = 143.479092554 Solving 17.5 + s = 143.479092554 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + s = 143.479092554 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + s = 143.479092554 + -17.5 s = 143.479092554 + -17.5 Combine like terms: 143.479092554 + -17.5 = 125.979092554 s = 125.979092554 Simplifying s = 125.979092554Subproblem 2
s + 17.5 = -143.479092554 Simplifying s + 17.5 = -143.479092554 Reorder the terms: 17.5 + s = -143.479092554 Solving 17.5 + s = -143.479092554 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + s = -143.479092554 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + s = -143.479092554 + -17.5 s = -143.479092554 + -17.5 Combine like terms: -143.479092554 + -17.5 = -160.979092554 s = -160.979092554 Simplifying s = -160.979092554Solution
The solution to the problem is based on the solutions from the subproblems. s = {125.979092554, -160.979092554}Solution
s = {125.979092554, -160.979092554}
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