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Simplifying 16s2 + 40s + -25 = 0 Reorder the terms: -25 + 40s + 16s2 = 0 Solving -25 + 40s + 16s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + 2.5s + s2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 2.5s + 1.5625 + s2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 2.5s + s2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 2.5s + s2 = 0 + 1.5625 2.5s + s2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 2.5s + s2 = 1.5625 The s term is 2.5s. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5s + 1.5625 + s2 = 1.5625 + 1.5625 Reorder the terms: 1.5625 + 2.5s + s2 = 1.5625 + 1.5625 Combine like terms: 1.5625 + 1.5625 = 3.125 1.5625 + 2.5s + s2 = 3.125 Factor a perfect square on the left side: (s + 1.25)(s + 1.25) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (s + 1.25) equal to 1.767766953 and -1.767766953.Subproblem 1
s + 1.25 = 1.767766953 Simplifying s + 1.25 = 1.767766953 Reorder the terms: 1.25 + s = 1.767766953 Solving 1.25 + s = 1.767766953 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + s = 1.767766953 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + s = 1.767766953 + -1.25 s = 1.767766953 + -1.25 Combine like terms: 1.767766953 + -1.25 = 0.517766953 s = 0.517766953 Simplifying s = 0.517766953Subproblem 2
s + 1.25 = -1.767766953 Simplifying s + 1.25 = -1.767766953 Reorder the terms: 1.25 + s = -1.767766953 Solving 1.25 + s = -1.767766953 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + s = -1.767766953 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + s = -1.767766953 + -1.25 s = -1.767766953 + -1.25 Combine like terms: -1.767766953 + -1.25 = -3.017766953 s = -3.017766953 Simplifying s = -3.017766953Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.517766953, -3.017766953}
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