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Simplifying 1 + -5r = -2r2 Solving 1 + -5r = -2r2 Solving for variable 'r'. Combine like terms: -2r2 + 2r2 = 0 1 + -5r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -2.5r + r2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -2.5r + -0.5 + r2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -2.5r + r2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2.5r + r2 = 0 + -0.5 -2.5r + r2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -2.5r + r2 = -0.5 The r term is -2.5r. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5r + 1.5625 + r2 = -0.5 + 1.5625 Reorder the terms: 1.5625 + -2.5r + r2 = -0.5 + 1.5625 Combine like terms: -0.5 + 1.5625 = 1.0625 1.5625 + -2.5r + r2 = 1.0625 Factor a perfect square on the left side: (r + -1.25)(r + -1.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (r + -1.25) equal to 1.030776406 and -1.030776406.Subproblem 1
r + -1.25 = 1.030776406 Simplifying r + -1.25 = 1.030776406 Reorder the terms: -1.25 + r = 1.030776406 Solving -1.25 + r = 1.030776406 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + r = 1.030776406 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + r = 1.030776406 + 1.25 r = 1.030776406 + 1.25 Combine like terms: 1.030776406 + 1.25 = 2.280776406 r = 2.280776406 Simplifying r = 2.280776406Subproblem 2
r + -1.25 = -1.030776406 Simplifying r + -1.25 = -1.030776406 Reorder the terms: -1.25 + r = -1.030776406 Solving -1.25 + r = -1.030776406 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + r = -1.030776406 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + r = -1.030776406 + 1.25 r = -1.030776406 + 1.25 Combine like terms: -1.030776406 + 1.25 = 0.219223594 r = 0.219223594 Simplifying r = 0.219223594Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.280776406, 0.219223594}
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