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Simplifying 6r(2r + -11) = 47 Reorder the terms: 6r(-11 + 2r) = 47 (-11 * 6r + 2r * 6r) = 47 (-66r + 12r2) = 47 Solving -66r + 12r2 = 47 Solving for variable 'r'. Reorder the terms: -47 + -66r + 12r2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + -66r + 12r2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.916666667 + -5.5r + r2 = 0 Move the constant term to the right: Add '3.916666667' to each side of the equation. -3.916666667 + -5.5r + 3.916666667 + r2 = 0 + 3.916666667 Reorder the terms: -3.916666667 + 3.916666667 + -5.5r + r2 = 0 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + -5.5r + r2 = 0 + 3.916666667 -5.5r + r2 = 0 + 3.916666667 Combine like terms: 0 + 3.916666667 = 3.916666667 -5.5r + r2 = 3.916666667 The r term is -5.5r. 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. -5.5r + 7.5625 + r2 = 3.916666667 + 7.5625 Reorder the terms: 7.5625 + -5.5r + r2 = 3.916666667 + 7.5625 Combine like terms: 3.916666667 + 7.5625 = 11.479166667 7.5625 + -5.5r + r2 = 11.479166667 Factor a perfect square on the left side: (r + -2.75)(r + -2.75) = 11.479166667 Calculate the square root of the right side: 3.388091892 Break this problem into two subproblems by setting (r + -2.75) equal to 3.388091892 and -3.388091892.Subproblem 1
r + -2.75 = 3.388091892 Simplifying r + -2.75 = 3.388091892 Reorder the terms: -2.75 + r = 3.388091892 Solving -2.75 + r = 3.388091892 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + r = 3.388091892 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + r = 3.388091892 + 2.75 r = 3.388091892 + 2.75 Combine like terms: 3.388091892 + 2.75 = 6.138091892 r = 6.138091892 Simplifying r = 6.138091892Subproblem 2
r + -2.75 = -3.388091892 Simplifying r + -2.75 = -3.388091892 Reorder the terms: -2.75 + r = -3.388091892 Solving -2.75 + r = -3.388091892 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + r = -3.388091892 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + r = -3.388091892 + 2.75 r = -3.388091892 + 2.75 Combine like terms: -3.388091892 + 2.75 = -0.638091892 r = -0.638091892 Simplifying r = -0.638091892Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.138091892, -0.638091892}
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