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Simplifying (s) * 2(s + 3) + (4s + -5) = 148 Reorder the terms: s * 2(3 + s) + (4s + -5) = 148 Reorder the terms for easier multiplication: 2s(3 + s) + (4s + -5) = 148 (3 * 2s + s * 2s) + (4s + -5) = 148 (6s + 2s2) + (4s + -5) = 148 Reorder the terms: 6s + 2s2 + (-5 + 4s) = 148 Remove parenthesis around (-5 + 4s) 6s + 2s2 + -5 + 4s = 148 Reorder the terms: -5 + 6s + 4s + 2s2 = 148 Combine like terms: 6s + 4s = 10s -5 + 10s + 2s2 = 148 Solving -5 + 10s + 2s2 = 148 Solving for variable 's'. Reorder the terms: -5 + -148 + 10s + 2s2 = 148 + -148 Combine like terms: -5 + -148 = -153 -153 + 10s + 2s2 = 148 + -148 Combine like terms: 148 + -148 = 0 -153 + 10s + 2s2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -76.5 + 5s + s2 = 0 Move the constant term to the right: Add '76.5' to each side of the equation. -76.5 + 5s + 76.5 + s2 = 0 + 76.5 Reorder the terms: -76.5 + 76.5 + 5s + s2 = 0 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + 5s + s2 = 0 + 76.5 5s + s2 = 0 + 76.5 Combine like terms: 0 + 76.5 = 76.5 5s + s2 = 76.5 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 = 76.5 + 6.25 Reorder the terms: 6.25 + 5s + s2 = 76.5 + 6.25 Combine like terms: 76.5 + 6.25 = 82.75 6.25 + 5s + s2 = 82.75 Factor a perfect square on the left side: (s + 2.5)(s + 2.5) = 82.75 Calculate the square root of the right side: 9.096702699 Break this problem into two subproblems by setting (s + 2.5) equal to 9.096702699 and -9.096702699.Subproblem 1
s + 2.5 = 9.096702699 Simplifying s + 2.5 = 9.096702699 Reorder the terms: 2.5 + s = 9.096702699 Solving 2.5 + s = 9.096702699 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 = 9.096702699 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = 9.096702699 + -2.5 s = 9.096702699 + -2.5 Combine like terms: 9.096702699 + -2.5 = 6.596702699 s = 6.596702699 Simplifying s = 6.596702699Subproblem 2
s + 2.5 = -9.096702699 Simplifying s + 2.5 = -9.096702699 Reorder the terms: 2.5 + s = -9.096702699 Solving 2.5 + s = -9.096702699 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 = -9.096702699 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + s = -9.096702699 + -2.5 s = -9.096702699 + -2.5 Combine like terms: -9.096702699 + -2.5 = -11.596702699 s = -11.596702699 Simplifying s = -11.596702699Solution
The solution to the problem is based on the solutions from the subproblems. s = {6.596702699, -11.596702699}
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