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Simplifying 7s + 2 = 4s(s + 1) Reorder the terms: 2 + 7s = 4s(s + 1) Reorder the terms: 2 + 7s = 4s(1 + s) 2 + 7s = (1 * 4s + s * 4s) 2 + 7s = (4s + 4s2) Solving 2 + 7s = 4s + 4s2 Solving for variable 's'. Combine like terms: 7s + -4s = 3s 2 + 3s + -4s2 = 4s + 4s2 + -4s + -4s2 Reorder the terms: 2 + 3s + -4s2 = 4s + -4s + 4s2 + -4s2 Combine like terms: 4s + -4s = 0 2 + 3s + -4s2 = 0 + 4s2 + -4s2 2 + 3s + -4s2 = 4s2 + -4s2 Combine like terms: 4s2 + -4s2 = 0 2 + 3s + -4s2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.5 + -0.75s + s2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.75s + 0.5 + s2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.75s + s2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.75s + s2 = 0 + 0.5 -0.75s + s2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.75s + s2 = 0.5 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 = 0.5 + 0.140625 Reorder the terms: 0.140625 + -0.75s + s2 = 0.5 + 0.140625 Combine like terms: 0.5 + 0.140625 = 0.640625 0.140625 + -0.75s + s2 = 0.640625 Factor a perfect square on the left side: (s + -0.375)(s + -0.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (s + -0.375) equal to 0.80039053 and -0.80039053.Subproblem 1
s + -0.375 = 0.80039053 Simplifying s + -0.375 = 0.80039053 Reorder the terms: -0.375 + s = 0.80039053 Solving -0.375 + s = 0.80039053 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 = 0.80039053 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + s = 0.80039053 + 0.375 s = 0.80039053 + 0.375 Combine like terms: 0.80039053 + 0.375 = 1.17539053 s = 1.17539053 Simplifying s = 1.17539053Subproblem 2
s + -0.375 = -0.80039053 Simplifying s + -0.375 = -0.80039053 Reorder the terms: -0.375 + s = -0.80039053 Solving -0.375 + s = -0.80039053 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 = -0.80039053 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + s = -0.80039053 + 0.375 s = -0.80039053 + 0.375 Combine like terms: -0.80039053 + 0.375 = -0.42539053 s = -0.42539053 Simplifying s = -0.42539053Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.17539053, -0.42539053}
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