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Simplifying 19r2 + 19r + -35 = 0 Reorder the terms: -35 + 19r + 19r2 = 0 Solving -35 + 19r + 19r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -1.842105263 + r + r2 = 0 Move the constant term to the right: Add '1.842105263' to each side of the equation. -1.842105263 + r + 1.842105263 + r2 = 0 + 1.842105263 Reorder the terms: -1.842105263 + 1.842105263 + r + r2 = 0 + 1.842105263 Combine like terms: -1.842105263 + 1.842105263 = 0.000000000 0.000000000 + r + r2 = 0 + 1.842105263 r + r2 = 0 + 1.842105263 Combine like terms: 0 + 1.842105263 = 1.842105263 r + r2 = 1.842105263 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + r2 = 1.842105263 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + r2 = 1.842105263 + 0.25 Combine like terms: 1.842105263 + 0.25 = 2.092105263 1.25 + r2 = 2.092105263 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 2.092105263 Calculate the square root of the right side: 1.446411167 Break this problem into two subproblems by setting (r + 0.5) equal to 1.446411167 and -1.446411167.Subproblem 1
r + 0.5 = 1.446411167 Simplifying r + 0.5 = 1.446411167 Reorder the terms: 0.5 + r = 1.446411167 Solving 0.5 + r = 1.446411167 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 1.446411167 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 1.446411167 + -0.5 r = 1.446411167 + -0.5 Combine like terms: 1.446411167 + -0.5 = 0.946411167 r = 0.946411167 Simplifying r = 0.946411167Subproblem 2
r + 0.5 = -1.446411167 Simplifying r + 0.5 = -1.446411167 Reorder the terms: 0.5 + r = -1.446411167 Solving 0.5 + r = -1.446411167 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -1.446411167 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -1.446411167 + -0.5 r = -1.446411167 + -0.5 Combine like terms: -1.446411167 + -0.5 = -1.946411167 r = -1.946411167 Simplifying r = -1.946411167Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.946411167, -1.946411167}
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