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Simplifying s2 + -4s = 16 + 25 Reorder the terms: -4s + s2 = 16 + 25 Combine like terms: 16 + 25 = 41 -4s + s2 = 41 Solving -4s + s2 = 41 Solving for variable 's'. Reorder the terms: -41 + -4s + s2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + -4s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -4s + 41 + s2 = 0 + 41 Reorder the terms: -41 + 41 + -4s + s2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -4s + s2 = 0 + 41 -4s + s2 = 0 + 41 Combine like terms: 0 + 41 = 41 -4s + s2 = 41 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 = 41 + 4 Reorder the terms: 4 + -4s + s2 = 41 + 4 Combine like terms: 41 + 4 = 45 4 + -4s + s2 = 45 Factor a perfect square on the left side: (s + -2)(s + -2) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (s + -2) equal to 6.708203933 and -6.708203933.Subproblem 1
s + -2 = 6.708203933 Simplifying s + -2 = 6.708203933 Reorder the terms: -2 + s = 6.708203933 Solving -2 + s = 6.708203933 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 = 6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + s = 6.708203933 + 2 s = 6.708203933 + 2 Combine like terms: 6.708203933 + 2 = 8.708203933 s = 8.708203933 Simplifying s = 8.708203933Subproblem 2
s + -2 = -6.708203933 Simplifying s + -2 = -6.708203933 Reorder the terms: -2 + s = -6.708203933 Solving -2 + s = -6.708203933 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 = -6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + s = -6.708203933 + 2 s = -6.708203933 + 2 Combine like terms: -6.708203933 + 2 = -4.708203933 s = -4.708203933 Simplifying s = -4.708203933Solution
The solution to the problem is based on the solutions from the subproblems. s = {8.708203933, -4.708203933}
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