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Simplifying s(2s + -13) = 94 Reorder the terms: s(-13 + 2s) = 94 (-13 * s + 2s * s) = 94 (-13s + 2s2) = 94 Solving -13s + 2s2 = 94 Solving for variable 's'. Reorder the terms: -94 + -13s + 2s2 = 94 + -94 Combine like terms: 94 + -94 = 0 -94 + -13s + 2s2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -47 + -6.5s + s2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + -6.5s + 47 + s2 = 0 + 47 Reorder the terms: -47 + 47 + -6.5s + s2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -6.5s + s2 = 0 + 47 -6.5s + s2 = 0 + 47 Combine like terms: 0 + 47 = 47 -6.5s + s2 = 47 The s term is -6.5s. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5s + 10.5625 + s2 = 47 + 10.5625 Reorder the terms: 10.5625 + -6.5s + s2 = 47 + 10.5625 Combine like terms: 47 + 10.5625 = 57.5625 10.5625 + -6.5s + s2 = 57.5625 Factor a perfect square on the left side: (s + -3.25)(s + -3.25) = 57.5625 Calculate the square root of the right side: 7.586995453 Break this problem into two subproblems by setting (s + -3.25) equal to 7.586995453 and -7.586995453.Subproblem 1
s + -3.25 = 7.586995453 Simplifying s + -3.25 = 7.586995453 Reorder the terms: -3.25 + s = 7.586995453 Solving -3.25 + s = 7.586995453 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + s = 7.586995453 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + s = 7.586995453 + 3.25 s = 7.586995453 + 3.25 Combine like terms: 7.586995453 + 3.25 = 10.836995453 s = 10.836995453 Simplifying s = 10.836995453Subproblem 2
s + -3.25 = -7.586995453 Simplifying s + -3.25 = -7.586995453 Reorder the terms: -3.25 + s = -7.586995453 Solving -3.25 + s = -7.586995453 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + s = -7.586995453 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + s = -7.586995453 + 3.25 s = -7.586995453 + 3.25 Combine like terms: -7.586995453 + 3.25 = -4.336995453 s = -4.336995453 Simplifying s = -4.336995453Solution
The solution to the problem is based on the solutions from the subproblems. s = {10.836995453, -4.336995453}
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