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Simplifying 2(4s + -16) * 5s = -5.2 Reorder the terms: 2(-16 + 4s) * 5s = -5.2 Reorder the terms for easier multiplication: 2 * 5s(-16 + 4s) = -5.2 Multiply 2 * 5 10s(-16 + 4s) = -5.2 (-16 * 10s + 4s * 10s) = -5.2 (-160s + 40s2) = -5.2 Solving -160s + 40s2 = -5.2 Solving for variable 's'. Reorder the terms: 5.2 + -160s + 40s2 = -5.2 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 5.2 + -160s + 40s2 = 0.0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.13 + -4s + s2 = 0.00 Move the constant term to the right: Add '-0.13' to each side of the equation. 0.13 + -4s + -0.13 + s2 = 0.00 + -0.13 Reorder the terms: 0.13 + -0.13 + -4s + s2 = 0.00 + -0.13 Combine like terms: 0.13 + -0.13 = 0.00 0.00 + -4s + s2 = 0.00 + -0.13 -4s + s2 = 0.00 + -0.13 Combine like terms: 0.00 + -0.13 = -0.13 -4s + s2 = -0.13 The s term is -4s. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4s + 4 + s2 = -0.13 + 4 Reorder the terms: 4 + -4s + s2 = -0.13 + 4 Combine like terms: -0.13 + 4 = 3.87 4 + -4s + s2 = 3.87 Factor a perfect square on the left side: (s + -2)(s + -2) = 3.87 Calculate the square root of the right side: 1.967231557 Break this problem into two subproblems by setting (s + -2) equal to 1.967231557 and -1.967231557.Subproblem 1
s + -2 = 1.967231557 Simplifying s + -2 = 1.967231557 Reorder the terms: -2 + s = 1.967231557 Solving -2 + s = 1.967231557 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + s = 1.967231557 + 2 Combine like terms: -2 + 2 = 0 0 + s = 1.967231557 + 2 s = 1.967231557 + 2 Combine like terms: 1.967231557 + 2 = 3.967231557 s = 3.967231557 Simplifying s = 3.967231557Subproblem 2
s + -2 = -1.967231557 Simplifying s + -2 = -1.967231557 Reorder the terms: -2 + s = -1.967231557 Solving -2 + s = -1.967231557 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + s = -1.967231557 + 2 Combine like terms: -2 + 2 = 0 0 + s = -1.967231557 + 2 s = -1.967231557 + 2 Combine like terms: -1.967231557 + 2 = 0.032768443 s = 0.032768443 Simplifying s = 0.032768443Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.967231557, 0.032768443}
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