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Simplifying 2s(s + -3) = 4s + 5 Reorder the terms: 2s(-3 + s) = 4s + 5 (-3 * 2s + s * 2s) = 4s + 5 (-6s + 2s2) = 4s + 5 Reorder the terms: -6s + 2s2 = 5 + 4s Solving -6s + 2s2 = 5 + 4s Solving for variable 's'. Reorder the terms: -5 + -6s + -4s + 2s2 = 5 + 4s + -5 + -4s Combine like terms: -6s + -4s = -10s -5 + -10s + 2s2 = 5 + 4s + -5 + -4s Reorder the terms: -5 + -10s + 2s2 = 5 + -5 + 4s + -4s Combine like terms: 5 + -5 = 0 -5 + -10s + 2s2 = 0 + 4s + -4s -5 + -10s + 2s2 = 4s + -4s Combine like terms: 4s + -4s = 0 -5 + -10s + 2s2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -5s + s2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -5s + 2.5 + s2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -5s + s2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -5s + s2 = 0 + 2.5 -5s + s2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -5s + s2 = 2.5 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 = 2.5 + 6.25 Reorder the terms: 6.25 + -5s + s2 = 2.5 + 6.25 Combine like terms: 2.5 + 6.25 = 8.75 6.25 + -5s + s2 = 8.75 Factor a perfect square on the left side: (s + -2.5)(s + -2.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (s + -2.5) equal to 2.958039892 and -2.958039892.Subproblem 1
s + -2.5 = 2.958039892 Simplifying s + -2.5 = 2.958039892 Reorder the terms: -2.5 + s = 2.958039892 Solving -2.5 + s = 2.958039892 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 = 2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + s = 2.958039892 + 2.5 s = 2.958039892 + 2.5 Combine like terms: 2.958039892 + 2.5 = 5.458039892 s = 5.458039892 Simplifying s = 5.458039892Subproblem 2
s + -2.5 = -2.958039892 Simplifying s + -2.5 = -2.958039892 Reorder the terms: -2.5 + s = -2.958039892 Solving -2.5 + s = -2.958039892 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 = -2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + s = -2.958039892 + 2.5 s = -2.958039892 + 2.5 Combine like terms: -2.958039892 + 2.5 = -0.458039892 s = -0.458039892 Simplifying s = -0.458039892Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.458039892, -0.458039892}
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