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Simplifying (5r2 + -13r + 2) = 0 Reorder the terms: (2 + -13r + 5r2) = 0 Remove parenthesis around (2 + -13r + 5r2) 2 + -13r + 5r2 = 0 Solving 2 + -13r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -2.6r + r2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -2.6r + -0.4 + r2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -2.6r + r2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -2.6r + r2 = 0 + -0.4 -2.6r + r2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -2.6r + r2 = -0.4 The r term is -2.6r. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6r + 1.69 + r2 = -0.4 + 1.69 Reorder the terms: 1.69 + -2.6r + r2 = -0.4 + 1.69 Combine like terms: -0.4 + 1.69 = 1.29 1.69 + -2.6r + r2 = 1.29 Factor a perfect square on the left side: (r + -1.3)(r + -1.3) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (r + -1.3) equal to 1.135781669 and -1.135781669.Subproblem 1
r + -1.3 = 1.135781669 Simplifying r + -1.3 = 1.135781669 Reorder the terms: -1.3 + r = 1.135781669 Solving -1.3 + r = 1.135781669 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + r = 1.135781669 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + r = 1.135781669 + 1.3 r = 1.135781669 + 1.3 Combine like terms: 1.135781669 + 1.3 = 2.435781669 r = 2.435781669 Simplifying r = 2.435781669Subproblem 2
r + -1.3 = -1.135781669 Simplifying r + -1.3 = -1.135781669 Reorder the terms: -1.3 + r = -1.135781669 Solving -1.3 + r = -1.135781669 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + r = -1.135781669 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + r = -1.135781669 + 1.3 r = -1.135781669 + 1.3 Combine like terms: -1.135781669 + 1.3 = 0.164218331 r = 0.164218331 Simplifying r = 0.164218331Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.435781669, 0.164218331}
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