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Simplifying 6s(2s + -11) = 47 Reorder the terms: 6s(-11 + 2s) = 47 (-11 * 6s + 2s * 6s) = 47 (-66s + 12s2) = 47 Solving -66s + 12s2 = 47 Solving for variable 's'. Reorder the terms: -47 + -66s + 12s2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + -66s + 12s2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.916666667 + -5.5s + s2 = 0 Move the constant term to the right: Add '3.916666667' to each side of the equation. -3.916666667 + -5.5s + 3.916666667 + s2 = 0 + 3.916666667 Reorder the terms: -3.916666667 + 3.916666667 + -5.5s + s2 = 0 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + -5.5s + s2 = 0 + 3.916666667 -5.5s + s2 = 0 + 3.916666667 Combine like terms: 0 + 3.916666667 = 3.916666667 -5.5s + s2 = 3.916666667 The s term is -5.5s. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5s + 7.5625 + s2 = 3.916666667 + 7.5625 Reorder the terms: 7.5625 + -5.5s + s2 = 3.916666667 + 7.5625 Combine like terms: 3.916666667 + 7.5625 = 11.479166667 7.5625 + -5.5s + s2 = 11.479166667 Factor a perfect square on the left side: (s + -2.75)(s + -2.75) = 11.479166667 Calculate the square root of the right side: 3.388091892 Break this problem into two subproblems by setting (s + -2.75) equal to 3.388091892 and -3.388091892.Subproblem 1
s + -2.75 = 3.388091892 Simplifying s + -2.75 = 3.388091892 Reorder the terms: -2.75 + s = 3.388091892 Solving -2.75 + s = 3.388091892 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + s = 3.388091892 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + s = 3.388091892 + 2.75 s = 3.388091892 + 2.75 Combine like terms: 3.388091892 + 2.75 = 6.138091892 s = 6.138091892 Simplifying s = 6.138091892Subproblem 2
s + -2.75 = -3.388091892 Simplifying s + -2.75 = -3.388091892 Reorder the terms: -2.75 + s = -3.388091892 Solving -2.75 + s = -3.388091892 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + s = -3.388091892 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + s = -3.388091892 + 2.75 s = -3.388091892 + 2.75 Combine like terms: -3.388091892 + 2.75 = -0.638091892 s = -0.638091892 Simplifying s = -0.638091892Solution
The solution to the problem is based on the solutions from the subproblems. s = {6.138091892, -0.638091892}
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