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Simplifying 4r2 + -20r = 0.25 Reorder the terms: -20r + 4r2 = 0.25 Solving -20r + 4r2 = 0.25 Solving for variable 'r'. Reorder the terms: -0.25 + -20r + 4r2 = 0.25 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 -0.25 + -20r + 4r2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.0625 + -5r + r2 = 0.00 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -5r + 0.0625 + r2 = 0.00 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -5r + r2 = 0.00 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -5r + r2 = 0.00 + 0.0625 -5r + r2 = 0.00 + 0.0625 Combine like terms: 0.00 + 0.0625 = 0.0625 -5r + r2 = 0.0625 The r term is -5r. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5r + 6.25 + r2 = 0.0625 + 6.25 Reorder the terms: 6.25 + -5r + r2 = 0.0625 + 6.25 Combine like terms: 0.0625 + 6.25 = 6.3125 6.25 + -5r + r2 = 6.3125 Factor a perfect square on the left side: (r + -2.5)(r + -2.5) = 6.3125 Calculate the square root of the right side: 2.512468905 Break this problem into two subproblems by setting (r + -2.5) equal to 2.512468905 and -2.512468905.Subproblem 1
r + -2.5 = 2.512468905 Simplifying r + -2.5 = 2.512468905 Reorder the terms: -2.5 + r = 2.512468905 Solving -2.5 + r = 2.512468905 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = 2.512468905 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = 2.512468905 + 2.5 r = 2.512468905 + 2.5 Combine like terms: 2.512468905 + 2.5 = 5.012468905 r = 5.012468905 Simplifying r = 5.012468905Subproblem 2
r + -2.5 = -2.512468905 Simplifying r + -2.5 = -2.512468905 Reorder the terms: -2.5 + r = -2.512468905 Solving -2.5 + r = -2.512468905 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = -2.512468905 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = -2.512468905 + 2.5 r = -2.512468905 + 2.5 Combine like terms: -2.512468905 + 2.5 = -0.012468905 r = -0.012468905 Simplifying r = -0.012468905Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.012468905, -0.012468905}
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