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Simplifying 5 + -3r2 = -12r Solving 5 + -3r2 = -12r Solving for variable 'r'. Reorder the terms: 5 + 12r + -3r2 = -12r + 12r Combine like terms: -12r + 12r = 0 5 + 12r + -3r2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + -4r + r2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -4r + 1.666666667 + r2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -4r + r2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -4r + r2 = 0 + 1.666666667 -4r + r2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -4r + r2 = 1.666666667 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = 1.666666667 + 4 Reorder the terms: 4 + -4r + r2 = 1.666666667 + 4 Combine like terms: 1.666666667 + 4 = 5.666666667 4 + -4r + r2 = 5.666666667 Factor a perfect square on the left side: (r + -2)(r + -2) = 5.666666667 Calculate the square root of the right side: 2.380476143 Break this problem into two subproblems by setting (r + -2) equal to 2.380476143 and -2.380476143.Subproblem 1
r + -2 = 2.380476143 Simplifying r + -2 = 2.380476143 Reorder the terms: -2 + r = 2.380476143 Solving -2 + r = 2.380476143 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 2.380476143 + 2 Combine like terms: -2 + 2 = 0 0 + r = 2.380476143 + 2 r = 2.380476143 + 2 Combine like terms: 2.380476143 + 2 = 4.380476143 r = 4.380476143 Simplifying r = 4.380476143Subproblem 2
r + -2 = -2.380476143 Simplifying r + -2 = -2.380476143 Reorder the terms: -2 + r = -2.380476143 Solving -2 + r = -2.380476143 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -2.380476143 + 2 Combine like terms: -2 + 2 = 0 0 + r = -2.380476143 + 2 r = -2.380476143 + 2 Combine like terms: -2.380476143 + 2 = -0.380476143 r = -0.380476143 Simplifying r = -0.380476143Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.380476143, -0.380476143}
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