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Simplifying 11r2 + -165r + 5 = 0 Reorder the terms: 5 + -165r + 11r2 = 0 Solving 5 + -165r + 11r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.4545454545 + -15r + r2 = 0 Move the constant term to the right: Add '-0.4545454545' to each side of the equation. 0.4545454545 + -15r + -0.4545454545 + r2 = 0 + -0.4545454545 Reorder the terms: 0.4545454545 + -0.4545454545 + -15r + r2 = 0 + -0.4545454545 Combine like terms: 0.4545454545 + -0.4545454545 = 0.0000000000 0.0000000000 + -15r + r2 = 0 + -0.4545454545 -15r + r2 = 0 + -0.4545454545 Combine like terms: 0 + -0.4545454545 = -0.4545454545 -15r + r2 = -0.4545454545 The r term is -15r. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15r + 56.25 + r2 = -0.4545454545 + 56.25 Reorder the terms: 56.25 + -15r + r2 = -0.4545454545 + 56.25 Combine like terms: -0.4545454545 + 56.25 = 55.7954545455 56.25 + -15r + r2 = 55.7954545455 Factor a perfect square on the left side: (r + -7.5)(r + -7.5) = 55.7954545455 Calculate the square root of the right side: 7.469635503 Break this problem into two subproblems by setting (r + -7.5) equal to 7.469635503 and -7.469635503.Subproblem 1
r + -7.5 = 7.469635503 Simplifying r + -7.5 = 7.469635503 Reorder the terms: -7.5 + r = 7.469635503 Solving -7.5 + r = 7.469635503 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + r = 7.469635503 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + r = 7.469635503 + 7.5 r = 7.469635503 + 7.5 Combine like terms: 7.469635503 + 7.5 = 14.969635503 r = 14.969635503 Simplifying r = 14.969635503Subproblem 2
r + -7.5 = -7.469635503 Simplifying r + -7.5 = -7.469635503 Reorder the terms: -7.5 + r = -7.469635503 Solving -7.5 + r = -7.469635503 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + r = -7.469635503 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + r = -7.469635503 + 7.5 r = -7.469635503 + 7.5 Combine like terms: -7.469635503 + 7.5 = 0.030364497 r = 0.030364497 Simplifying r = 0.030364497Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.969635503, 0.030364497}
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