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Simplifying s2 + -95s + -905500 = 0 Reorder the terms: -905500 + -95s + s2 = 0 Solving -905500 + -95s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '905500' to each side of the equation. -905500 + -95s + 905500 + s2 = 0 + 905500 Reorder the terms: -905500 + 905500 + -95s + s2 = 0 + 905500 Combine like terms: -905500 + 905500 = 0 0 + -95s + s2 = 0 + 905500 -95s + s2 = 0 + 905500 Combine like terms: 0 + 905500 = 905500 -95s + s2 = 905500 The s term is -95s. Take half its coefficient (-47.5). Square it (2256.25) and add it to both sides. Add '2256.25' to each side of the equation. -95s + 2256.25 + s2 = 905500 + 2256.25 Reorder the terms: 2256.25 + -95s + s2 = 905500 + 2256.25 Combine like terms: 905500 + 2256.25 = 907756.25 2256.25 + -95s + s2 = 907756.25 Factor a perfect square on the left side: (s + -47.5)(s + -47.5) = 907756.25 Calculate the square root of the right side: 952.762431039 Break this problem into two subproblems by setting (s + -47.5) equal to 952.762431039 and -952.762431039.Subproblem 1
s + -47.5 = 952.762431039 Simplifying s + -47.5 = 952.762431039 Reorder the terms: -47.5 + s = 952.762431039 Solving -47.5 + s = 952.762431039 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '47.5' to each side of the equation. -47.5 + 47.5 + s = 952.762431039 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + s = 952.762431039 + 47.5 s = 952.762431039 + 47.5 Combine like terms: 952.762431039 + 47.5 = 1000.262431039 s = 1000.262431039 Simplifying s = 1000.262431039Subproblem 2
s + -47.5 = -952.762431039 Simplifying s + -47.5 = -952.762431039 Reorder the terms: -47.5 + s = -952.762431039 Solving -47.5 + s = -952.762431039 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '47.5' to each side of the equation. -47.5 + 47.5 + s = -952.762431039 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + s = -952.762431039 + 47.5 s = -952.762431039 + 47.5 Combine like terms: -952.762431039 + 47.5 = -905.262431039 s = -905.262431039 Simplifying s = -905.262431039Solution
The solution to the problem is based on the solutions from the subproblems. s = {1000.262431039, -905.262431039}
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