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Simplifying s2 + -30s + -40 = 0 Reorder the terms: -40 + -30s + s2 = 0 Solving -40 + -30s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -30s + 40 + s2 = 0 + 40 Reorder the terms: -40 + 40 + -30s + s2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -30s + s2 = 0 + 40 -30s + s2 = 0 + 40 Combine like terms: 0 + 40 = 40 -30s + s2 = 40 The s term is -30s. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30s + 225 + s2 = 40 + 225 Reorder the terms: 225 + -30s + s2 = 40 + 225 Combine like terms: 40 + 225 = 265 225 + -30s + s2 = 265 Factor a perfect square on the left side: (s + -15)(s + -15) = 265 Calculate the square root of the right side: 16.278820596 Break this problem into two subproblems by setting (s + -15) equal to 16.278820596 and -16.278820596.Subproblem 1
s + -15 = 16.278820596 Simplifying s + -15 = 16.278820596 Reorder the terms: -15 + s = 16.278820596 Solving -15 + s = 16.278820596 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + s = 16.278820596 + 15 Combine like terms: -15 + 15 = 0 0 + s = 16.278820596 + 15 s = 16.278820596 + 15 Combine like terms: 16.278820596 + 15 = 31.278820596 s = 31.278820596 Simplifying s = 31.278820596Subproblem 2
s + -15 = -16.278820596 Simplifying s + -15 = -16.278820596 Reorder the terms: -15 + s = -16.278820596 Solving -15 + s = -16.278820596 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + s = -16.278820596 + 15 Combine like terms: -15 + 15 = 0 0 + s = -16.278820596 + 15 s = -16.278820596 + 15 Combine like terms: -16.278820596 + 15 = -1.278820596 s = -1.278820596 Simplifying s = -1.278820596Solution
The solution to the problem is based on the solutions from the subproblems. s = {31.278820596, -1.278820596}
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