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Simplifying s2 + -25 = 10s + 25 Reorder the terms: -25 + s2 = 10s + 25 Reorder the terms: -25 + s2 = 25 + 10s Solving -25 + s2 = 25 + 10s Solving for variable 's'. Reorder the terms: -25 + -25 + -10s + s2 = 25 + 10s + -25 + -10s Combine like terms: -25 + -25 = -50 -50 + -10s + s2 = 25 + 10s + -25 + -10s Reorder the terms: -50 + -10s + s2 = 25 + -25 + 10s + -10s Combine like terms: 25 + -25 = 0 -50 + -10s + s2 = 0 + 10s + -10s -50 + -10s + s2 = 10s + -10s Combine like terms: 10s + -10s = 0 -50 + -10s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -10s + 50 + s2 = 0 + 50 Reorder the terms: -50 + 50 + -10s + s2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -10s + s2 = 0 + 50 -10s + s2 = 0 + 50 Combine like terms: 0 + 50 = 50 -10s + s2 = 50 The s term is -10s. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10s + 25 + s2 = 50 + 25 Reorder the terms: 25 + -10s + s2 = 50 + 25 Combine like terms: 50 + 25 = 75 25 + -10s + s2 = 75 Factor a perfect square on the left side: (s + -5)(s + -5) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (s + -5) equal to 8.660254038 and -8.660254038.Subproblem 1
s + -5 = 8.660254038 Simplifying s + -5 = 8.660254038 Reorder the terms: -5 + s = 8.660254038 Solving -5 + s = 8.660254038 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + s = 8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + s = 8.660254038 + 5 s = 8.660254038 + 5 Combine like terms: 8.660254038 + 5 = 13.660254038 s = 13.660254038 Simplifying s = 13.660254038Subproblem 2
s + -5 = -8.660254038 Simplifying s + -5 = -8.660254038 Reorder the terms: -5 + s = -8.660254038 Solving -5 + s = -8.660254038 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + s = -8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + s = -8.660254038 + 5 s = -8.660254038 + 5 Combine like terms: -8.660254038 + 5 = -3.660254038 s = -3.660254038 Simplifying s = -3.660254038Solution
The solution to the problem is based on the solutions from the subproblems. s = {13.660254038, -3.660254038}
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