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Simplifying 0.25s2 + 0.6s + 0.36 = 0 Reorder the terms: 0.36 + 0.6s + 0.25s2 = 0 Solving 0.36 + 0.6s + 0.25s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 1.44 + 2.4s + s2 = 0 Move the constant term to the right: Add '-1.44' to each side of the equation. 1.44 + 2.4s + -1.44 + s2 = 0 + -1.44 Reorder the terms: 1.44 + -1.44 + 2.4s + s2 = 0 + -1.44 Combine like terms: 1.44 + -1.44 = 0.00 0.00 + 2.4s + s2 = 0 + -1.44 2.4s + s2 = 0 + -1.44 Combine like terms: 0 + -1.44 = -1.44 2.4s + s2 = -1.44 The s term is 2.4s. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4s + 1.44 + s2 = -1.44 + 1.44 Reorder the terms: 1.44 + 2.4s + s2 = -1.44 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 1.44 + 2.4s + s2 = 0.00 Factor a perfect square on the left side: (s + 1.2)(s + 1.2) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (s + 1.2) equal to 0.00 and 0.00.Subproblem 1
s + 1.2 = 0.00 Simplifying s + 1.2 = 0.00 Reorder the terms: 1.2 + s = 0.00 Solving 1.2 + s = 0.00 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + s = 0.00 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + s = 0.00 + -1.2 s = 0.00 + -1.2 Combine like terms: 0.00 + -1.2 = -1.2 s = -1.2 Simplifying s = -1.2Subproblem 2
s + 1.2 = 0.00 Simplifying s + 1.2 = 0.00 Reorder the terms: 1.2 + s = 0.00 Solving 1.2 + s = 0.00 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + s = 0.00 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + s = 0.00 + -1.2 s = 0.00 + -1.2 Combine like terms: 0.00 + -1.2 = -1.2 s = -1.2 Simplifying s = -1.2Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.2, -1.2}
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