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Simplifying 19r2 + 20r + -475 = 0 Reorder the terms: -475 + 20r + 19r2 = 0 Solving -475 + 20r + 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'. -25 + 1.052631579r + r2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 1.052631579r + 25 + r2 = 0 + 25 Reorder the terms: -25 + 25 + 1.052631579r + r2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 1.052631579r + r2 = 0 + 25 1.052631579r + r2 = 0 + 25 Combine like terms: 0 + 25 = 25 1.052631579r + r2 = 25 The r term is 1.052631579r. Take half its coefficient (0.5263157895). Square it (0.2770083103) and add it to both sides. Add '0.2770083103' to each side of the equation. 1.052631579r + 0.2770083103 + r2 = 25 + 0.2770083103 Reorder the terms: 0.2770083103 + 1.052631579r + r2 = 25 + 0.2770083103 Combine like terms: 25 + 0.2770083103 = 25.2770083103 0.2770083103 + 1.052631579r + r2 = 25.2770083103 Factor a perfect square on the left side: (r + 0.5263157895)(r + 0.5263157895) = 25.2770083103 Calculate the square root of the right side: 5.02762452 Break this problem into two subproblems by setting (r + 0.5263157895) equal to 5.02762452 and -5.02762452.Subproblem 1
r + 0.5263157895 = 5.02762452 Simplifying r + 0.5263157895 = 5.02762452 Reorder the terms: 0.5263157895 + r = 5.02762452 Solving 0.5263157895 + r = 5.02762452 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5263157895' to each side of the equation. 0.5263157895 + -0.5263157895 + r = 5.02762452 + -0.5263157895 Combine like terms: 0.5263157895 + -0.5263157895 = 0.0000000000 0.0000000000 + r = 5.02762452 + -0.5263157895 r = 5.02762452 + -0.5263157895 Combine like terms: 5.02762452 + -0.5263157895 = 4.5013087305 r = 4.5013087305 Simplifying r = 4.5013087305Subproblem 2
r + 0.5263157895 = -5.02762452 Simplifying r + 0.5263157895 = -5.02762452 Reorder the terms: 0.5263157895 + r = -5.02762452 Solving 0.5263157895 + r = -5.02762452 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5263157895' to each side of the equation. 0.5263157895 + -0.5263157895 + r = -5.02762452 + -0.5263157895 Combine like terms: 0.5263157895 + -0.5263157895 = 0.0000000000 0.0000000000 + r = -5.02762452 + -0.5263157895 r = -5.02762452 + -0.5263157895 Combine like terms: -5.02762452 + -0.5263157895 = -5.5539403095 r = -5.5539403095 Simplifying r = -5.5539403095Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.5013087305, -5.5539403095}
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