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Simplifying 5r2 + -44r + 102 = -30 + 11r Reorder the terms: 102 + -44r + 5r2 = -30 + 11r Solving 102 + -44r + 5r2 = -30 + 11r Solving for variable 'r'. Reorder the terms: 102 + 30 + -44r + -11r + 5r2 = -30 + 11r + 30 + -11r Combine like terms: 102 + 30 = 132 132 + -44r + -11r + 5r2 = -30 + 11r + 30 + -11r Combine like terms: -44r + -11r = -55r 132 + -55r + 5r2 = -30 + 11r + 30 + -11r Reorder the terms: 132 + -55r + 5r2 = -30 + 30 + 11r + -11r Combine like terms: -30 + 30 = 0 132 + -55r + 5r2 = 0 + 11r + -11r 132 + -55r + 5r2 = 11r + -11r Combine like terms: 11r + -11r = 0 132 + -55r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 26.4 + -11r + r2 = 0 Move the constant term to the right: Add '-26.4' to each side of the equation. 26.4 + -11r + -26.4 + r2 = 0 + -26.4 Reorder the terms: 26.4 + -26.4 + -11r + r2 = 0 + -26.4 Combine like terms: 26.4 + -26.4 = 0.0 0.0 + -11r + r2 = 0 + -26.4 -11r + r2 = 0 + -26.4 Combine like terms: 0 + -26.4 = -26.4 -11r + r2 = -26.4 The r term is -11r. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11r + 30.25 + r2 = -26.4 + 30.25 Reorder the terms: 30.25 + -11r + r2 = -26.4 + 30.25 Combine like terms: -26.4 + 30.25 = 3.85 30.25 + -11r + r2 = 3.85 Factor a perfect square on the left side: (r + -5.5)(r + -5.5) = 3.85 Calculate the square root of the right side: 1.962141687 Break this problem into two subproblems by setting (r + -5.5) equal to 1.962141687 and -1.962141687.Subproblem 1
r + -5.5 = 1.962141687 Simplifying r + -5.5 = 1.962141687 Reorder the terms: -5.5 + r = 1.962141687 Solving -5.5 + r = 1.962141687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = 1.962141687 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = 1.962141687 + 5.5 r = 1.962141687 + 5.5 Combine like terms: 1.962141687 + 5.5 = 7.462141687 r = 7.462141687 Simplifying r = 7.462141687Subproblem 2
r + -5.5 = -1.962141687 Simplifying r + -5.5 = -1.962141687 Reorder the terms: -5.5 + r = -1.962141687 Solving -5.5 + r = -1.962141687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = -1.962141687 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = -1.962141687 + 5.5 r = -1.962141687 + 5.5 Combine like terms: -1.962141687 + 5.5 = 3.537858313 r = 3.537858313 Simplifying r = 3.537858313Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.462141687, 3.537858313}
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