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Simplifying 6r2 + 12r + -92 = 0 Reorder the terms: -92 + 12r + 6r2 = 0 Solving -92 + 12r + 6r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-46 + 6r + 3r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-46 + 6r + 3r2)' equal to zero and attempt to solve: Simplifying -46 + 6r + 3r2 = 0 Solving -46 + 6r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15.33333333 + 2r + r2 = 0 Move the constant term to the right: Add '15.33333333' to each side of the equation. -15.33333333 + 2r + 15.33333333 + r2 = 0 + 15.33333333 Reorder the terms: -15.33333333 + 15.33333333 + 2r + r2 = 0 + 15.33333333 Combine like terms: -15.33333333 + 15.33333333 = 0.00000000 0.00000000 + 2r + r2 = 0 + 15.33333333 2r + r2 = 0 + 15.33333333 Combine like terms: 0 + 15.33333333 = 15.33333333 2r + r2 = 15.33333333 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 15.33333333 + 1 Reorder the terms: 1 + 2r + r2 = 15.33333333 + 1 Combine like terms: 15.33333333 + 1 = 16.33333333 1 + 2r + r2 = 16.33333333 Factor a perfect square on the left side: (r + 1)(r + 1) = 16.33333333 Calculate the square root of the right side: 4.041451884 Break this problem into two subproblems by setting (r + 1) equal to 4.041451884 and -4.041451884.Subproblem 1
r + 1 = 4.041451884 Simplifying r + 1 = 4.041451884 Reorder the terms: 1 + r = 4.041451884 Solving 1 + r = 4.041451884 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 4.041451884 + -1 Combine like terms: 1 + -1 = 0 0 + r = 4.041451884 + -1 r = 4.041451884 + -1 Combine like terms: 4.041451884 + -1 = 3.041451884 r = 3.041451884 Simplifying r = 3.041451884Subproblem 2
r + 1 = -4.041451884 Simplifying r + 1 = -4.041451884 Reorder the terms: 1 + r = -4.041451884 Solving 1 + r = -4.041451884 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -4.041451884 + -1 Combine like terms: 1 + -1 = 0 0 + r = -4.041451884 + -1 r = -4.041451884 + -1 Combine like terms: -4.041451884 + -1 = -5.041451884 r = -5.041451884 Simplifying r = -5.041451884Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.041451884, -5.041451884}Solution
r = {3.041451884, -5.041451884}
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