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Simplifying s2 + 5s + 6.25 = 0 Reorder the terms: 6.25 + 5s + s2 = 0 Solving 6.25 + 5s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 5s + -6.25 + s2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 5s + s2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 5s + s2 = 0 + -6.25 5s + s2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 5s + s2 = -6.25 The s term is 5s. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5s + 6.25 + s2 = -6.25 + 6.25 Reorder the terms: 6.25 + 5s + s2 = -6.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 6.25 + 5s + s2 = 0.00 Factor a perfect square on the left side: (s + 2.5)(s + 2.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (s + 2.5) equal to 0.00 and 0.00.Subproblem 1
s + 2.5 = 0.00 Simplifying s + 2.5 = 0.00 Reorder the terms: 2.5 + s = 0.00 Solving 2.5 + s = 0.00 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + s = 0.00 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = 0.00 + -2.5 s = 0.00 + -2.5 Combine like terms: 0.00 + -2.5 = -2.5 s = -2.5 Simplifying s = -2.5Subproblem 2
s + 2.5 = 0.00 Simplifying s + 2.5 = 0.00 Reorder the terms: 2.5 + s = 0.00 Solving 2.5 + s = 0.00 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + s = 0.00 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = 0.00 + -2.5 s = 0.00 + -2.5 Combine like terms: 0.00 + -2.5 = -2.5 s = -2.5 Simplifying s = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. s = {-2.5, -2.5}
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