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Simplifying 5r2 + -25r = 17 Reorder the terms: -25r + 5r2 = 17 Solving -25r + 5r2 = 17 Solving for variable 'r'. Reorder the terms: -17 + -25r + 5r2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -25r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + -5r + r2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -5r + 3.4 + r2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -5r + r2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -5r + r2 = 0 + 3.4 -5r + r2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -5r + r2 = 3.4 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 = 3.4 + 6.25 Reorder the terms: 6.25 + -5r + r2 = 3.4 + 6.25 Combine like terms: 3.4 + 6.25 = 9.65 6.25 + -5r + r2 = 9.65 Factor a perfect square on the left side: (r + -2.5)(r + -2.5) = 9.65 Calculate the square root of the right side: 3.106444913 Break this problem into two subproblems by setting (r + -2.5) equal to 3.106444913 and -3.106444913.Subproblem 1
r + -2.5 = 3.106444913 Simplifying r + -2.5 = 3.106444913 Reorder the terms: -2.5 + r = 3.106444913 Solving -2.5 + r = 3.106444913 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 = 3.106444913 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = 3.106444913 + 2.5 r = 3.106444913 + 2.5 Combine like terms: 3.106444913 + 2.5 = 5.606444913 r = 5.606444913 Simplifying r = 5.606444913Subproblem 2
r + -2.5 = -3.106444913 Simplifying r + -2.5 = -3.106444913 Reorder the terms: -2.5 + r = -3.106444913 Solving -2.5 + r = -3.106444913 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 = -3.106444913 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = -3.106444913 + 2.5 r = -3.106444913 + 2.5 Combine like terms: -3.106444913 + 2.5 = -0.606444913 r = -0.606444913 Simplifying r = -0.606444913Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.606444913, -0.606444913}
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