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Simplifying 4r2 = 17r + 1 Reorder the terms: 4r2 = 1 + 17r Solving 4r2 = 1 + 17r Solving for variable 'r'. Reorder the terms: -1 + -17r + 4r2 = 1 + 17r + -1 + -17r Reorder the terms: -1 + -17r + 4r2 = 1 + -1 + 17r + -17r Combine like terms: 1 + -1 = 0 -1 + -17r + 4r2 = 0 + 17r + -17r -1 + -17r + 4r2 = 17r + -17r Combine like terms: 17r + -17r = 0 -1 + -17r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -4.25r + r2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -4.25r + 0.25 + r2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -4.25r + r2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -4.25r + r2 = 0 + 0.25 -4.25r + r2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -4.25r + r2 = 0.25 The r term is -4.25r. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25r + 4.515625 + r2 = 0.25 + 4.515625 Reorder the terms: 4.515625 + -4.25r + r2 = 0.25 + 4.515625 Combine like terms: 0.25 + 4.515625 = 4.765625 4.515625 + -4.25r + r2 = 4.765625 Factor a perfect square on the left side: (r + -2.125)(r + -2.125) = 4.765625 Calculate the square root of the right side: 2.18303115 Break this problem into two subproblems by setting (r + -2.125) equal to 2.18303115 and -2.18303115.Subproblem 1
r + -2.125 = 2.18303115 Simplifying r + -2.125 = 2.18303115 Reorder the terms: -2.125 + r = 2.18303115 Solving -2.125 + r = 2.18303115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + r = 2.18303115 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + r = 2.18303115 + 2.125 r = 2.18303115 + 2.125 Combine like terms: 2.18303115 + 2.125 = 4.30803115 r = 4.30803115 Simplifying r = 4.30803115Subproblem 2
r + -2.125 = -2.18303115 Simplifying r + -2.125 = -2.18303115 Reorder the terms: -2.125 + r = -2.18303115 Solving -2.125 + r = -2.18303115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + r = -2.18303115 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + r = -2.18303115 + 2.125 r = -2.18303115 + 2.125 Combine like terms: -2.18303115 + 2.125 = -0.05803115 r = -0.05803115 Simplifying r = -0.05803115Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.30803115, -0.05803115}
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