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Simplifying s2 + 4s + -40 = 0 Reorder the terms: -40 + 4s + s2 = 0 Solving -40 + 4s + 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 + 4s + 40 + s2 = 0 + 40 Reorder the terms: -40 + 40 + 4s + s2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 4s + s2 = 0 + 40 4s + s2 = 0 + 40 Combine like terms: 0 + 40 = 40 4s + s2 = 40 The s term is 4s. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4s + 4 + s2 = 40 + 4 Reorder the terms: 4 + 4s + s2 = 40 + 4 Combine like terms: 40 + 4 = 44 4 + 4s + s2 = 44 Factor a perfect square on the left side: (s + 2)(s + 2) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (s + 2) equal to 6.633249581 and -6.633249581.Subproblem 1
s + 2 = 6.633249581 Simplifying s + 2 = 6.633249581 Reorder the terms: 2 + s = 6.633249581 Solving 2 + s = 6.633249581 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = 6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + s = 6.633249581 + -2 s = 6.633249581 + -2 Combine like terms: 6.633249581 + -2 = 4.633249581 s = 4.633249581 Simplifying s = 4.633249581Subproblem 2
s + 2 = -6.633249581 Simplifying s + 2 = -6.633249581 Reorder the terms: 2 + s = -6.633249581 Solving 2 + s = -6.633249581 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = -6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + s = -6.633249581 + -2 s = -6.633249581 + -2 Combine like terms: -6.633249581 + -2 = -8.633249581 s = -8.633249581 Simplifying s = -8.633249581Solution
The solution to the problem is based on the solutions from the subproblems. s = {4.633249581, -8.633249581}
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