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Simplifying 4r2 + -104r + 5 = 0 Reorder the terms: 5 + -104r + 4r2 = 0 Solving 5 + -104r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -26r + r2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -26r + -1.25 + r2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -26r + r2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -26r + r2 = 0 + -1.25 -26r + r2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -26r + r2 = -1.25 The r term is -26r. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26r + 169 + r2 = -1.25 + 169 Reorder the terms: 169 + -26r + r2 = -1.25 + 169 Combine like terms: -1.25 + 169 = 167.75 169 + -26r + r2 = 167.75 Factor a perfect square on the left side: (r + -13)(r + -13) = 167.75 Calculate the square root of the right side: 12.951833847 Break this problem into two subproblems by setting (r + -13) equal to 12.951833847 and -12.951833847.Subproblem 1
r + -13 = 12.951833847 Simplifying r + -13 = 12.951833847 Reorder the terms: -13 + r = 12.951833847 Solving -13 + r = 12.951833847 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + r = 12.951833847 + 13 Combine like terms: -13 + 13 = 0 0 + r = 12.951833847 + 13 r = 12.951833847 + 13 Combine like terms: 12.951833847 + 13 = 25.951833847 r = 25.951833847 Simplifying r = 25.951833847Subproblem 2
r + -13 = -12.951833847 Simplifying r + -13 = -12.951833847 Reorder the terms: -13 + r = -12.951833847 Solving -13 + r = -12.951833847 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + r = -12.951833847 + 13 Combine like terms: -13 + 13 = 0 0 + r = -12.951833847 + 13 r = -12.951833847 + 13 Combine like terms: -12.951833847 + 13 = 0.048166153 r = 0.048166153 Simplifying r = 0.048166153Solution
The solution to the problem is based on the solutions from the subproblems. r = {25.951833847, 0.048166153}
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