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Simplifying 0 = r2 + 6r + -50.25 Reorder the terms: 0 = -50.25 + 6r + r2 Solving 0 = -50.25 + 6r + r2 Solving for variable 'r'. Combine like terms: 0 + 50.25 = 50.25 50.25 + -6r + -1r2 = -50.25 + 6r + r2 + 50.25 + -6r + -1r2 Reorder the terms: 50.25 + -6r + -1r2 = -50.25 + 50.25 + 6r + -6r + r2 + -1r2 Combine like terms: -50.25 + 50.25 = 0.00 50.25 + -6r + -1r2 = 0.00 + 6r + -6r + r2 + -1r2 50.25 + -6r + -1r2 = 6r + -6r + r2 + -1r2 Combine like terms: 6r + -6r = 0 50.25 + -6r + -1r2 = 0 + r2 + -1r2 50.25 + -6r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 50.25 + -6r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50.25 + 6r + r2 = 0 Move the constant term to the right: Add '50.25' to each side of the equation. -50.25 + 6r + 50.25 + r2 = 0 + 50.25 Reorder the terms: -50.25 + 50.25 + 6r + r2 = 0 + 50.25 Combine like terms: -50.25 + 50.25 = 0.00 0.00 + 6r + r2 = 0 + 50.25 6r + r2 = 0 + 50.25 Combine like terms: 0 + 50.25 = 50.25 6r + r2 = 50.25 The r term is 6r. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6r + 9 + r2 = 50.25 + 9 Reorder the terms: 9 + 6r + r2 = 50.25 + 9 Combine like terms: 50.25 + 9 = 59.25 9 + 6r + r2 = 59.25 Factor a perfect square on the left side: (r + 3)(r + 3) = 59.25 Calculate the square root of the right side: 7.697402159 Break this problem into two subproblems by setting (r + 3) equal to 7.697402159 and -7.697402159.Subproblem 1
r + 3 = 7.697402159 Simplifying r + 3 = 7.697402159 Reorder the terms: 3 + r = 7.697402159 Solving 3 + r = 7.697402159 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 7.697402159 + -3 Combine like terms: 3 + -3 = 0 0 + r = 7.697402159 + -3 r = 7.697402159 + -3 Combine like terms: 7.697402159 + -3 = 4.697402159 r = 4.697402159 Simplifying r = 4.697402159Subproblem 2
r + 3 = -7.697402159 Simplifying r + 3 = -7.697402159 Reorder the terms: 3 + r = -7.697402159 Solving 3 + r = -7.697402159 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -7.697402159 + -3 Combine like terms: 3 + -3 = 0 0 + r = -7.697402159 + -3 r = -7.697402159 + -3 Combine like terms: -7.697402159 + -3 = -10.697402159 r = -10.697402159 Simplifying r = -10.697402159Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.697402159, -10.697402159}
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