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Simplifying 148 = 2(s + 3) + (4s + -5) * s Reorder the terms: 148 = 2(3 + s) + (4s + -5) * s 148 = (3 * 2 + s * 2) + (4s + -5) * s 148 = (6 + 2s) + (4s + -5) * s Reorder the terms: 148 = 6 + 2s + (-5 + 4s) * s Reorder the terms for easier multiplication: 148 = 6 + 2s + s(-5 + 4s) 148 = 6 + 2s + (-5 * s + 4s * s) 148 = 6 + 2s + (-5s + 4s2) Combine like terms: 2s + -5s = -3s 148 = 6 + -3s + 4s2 Solving 148 = 6 + -3s + 4s2 Solving for variable 's'. Combine like terms: 148 + -6 = 142 142 + 3s + -4s2 = 6 + -3s + 4s2 + -6 + 3s + -4s2 Reorder the terms: 142 + 3s + -4s2 = 6 + -6 + -3s + 3s + 4s2 + -4s2 Combine like terms: 6 + -6 = 0 142 + 3s + -4s2 = 0 + -3s + 3s + 4s2 + -4s2 142 + 3s + -4s2 = -3s + 3s + 4s2 + -4s2 Combine like terms: -3s + 3s = 0 142 + 3s + -4s2 = 0 + 4s2 + -4s2 142 + 3s + -4s2 = 4s2 + -4s2 Combine like terms: 4s2 + -4s2 = 0 142 + 3s + -4s2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -35.5 + -0.75s + s2 = 0 Move the constant term to the right: Add '35.5' to each side of the equation. -35.5 + -0.75s + 35.5 + s2 = 0 + 35.5 Reorder the terms: -35.5 + 35.5 + -0.75s + s2 = 0 + 35.5 Combine like terms: -35.5 + 35.5 = 0.0 0.0 + -0.75s + s2 = 0 + 35.5 -0.75s + s2 = 0 + 35.5 Combine like terms: 0 + 35.5 = 35.5 -0.75s + s2 = 35.5 The s term is -0.75s. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75s + 0.140625 + s2 = 35.5 + 0.140625 Reorder the terms: 0.140625 + -0.75s + s2 = 35.5 + 0.140625 Combine like terms: 35.5 + 0.140625 = 35.640625 0.140625 + -0.75s + s2 = 35.640625 Factor a perfect square on the left side: (s + -0.375)(s + -0.375) = 35.640625 Calculate the square root of the right side: 5.969976968 Break this problem into two subproblems by setting (s + -0.375) equal to 5.969976968 and -5.969976968.Subproblem 1
s + -0.375 = 5.969976968 Simplifying s + -0.375 = 5.969976968 Reorder the terms: -0.375 + s = 5.969976968 Solving -0.375 + s = 5.969976968 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + s = 5.969976968 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + s = 5.969976968 + 0.375 s = 5.969976968 + 0.375 Combine like terms: 5.969976968 + 0.375 = 6.344976968 s = 6.344976968 Simplifying s = 6.344976968Subproblem 2
s + -0.375 = -5.969976968 Simplifying s + -0.375 = -5.969976968 Reorder the terms: -0.375 + s = -5.969976968 Solving -0.375 + s = -5.969976968 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + s = -5.969976968 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + s = -5.969976968 + 0.375 s = -5.969976968 + 0.375 Combine like terms: -5.969976968 + 0.375 = -5.594976968 s = -5.594976968 Simplifying s = -5.594976968Solution
The solution to the problem is based on the solutions from the subproblems. s = {6.344976968, -5.594976968}
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