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Simplifying 2r2 = 7r + -4 Reorder the terms: 2r2 = -4 + 7r Solving 2r2 = -4 + 7r Solving for variable 'r'. Reorder the terms: 4 + -7r + 2r2 = -4 + 7r + 4 + -7r Reorder the terms: 4 + -7r + 2r2 = -4 + 4 + 7r + -7r Combine like terms: -4 + 4 = 0 4 + -7r + 2r2 = 0 + 7r + -7r 4 + -7r + 2r2 = 7r + -7r Combine like terms: 7r + -7r = 0 4 + -7r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -3.5r + r2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.5r + -2 + r2 = 0 + -2 Reorder the terms: 2 + -2 + -3.5r + r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.5r + r2 = 0 + -2 -3.5r + r2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.5r + r2 = -2 The r term is -3.5r. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5r + 3.0625 + r2 = -2 + 3.0625 Reorder the terms: 3.0625 + -3.5r + r2 = -2 + 3.0625 Combine like terms: -2 + 3.0625 = 1.0625 3.0625 + -3.5r + r2 = 1.0625 Factor a perfect square on the left side: (r + -1.75)(r + -1.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (r + -1.75) equal to 1.030776406 and -1.030776406.Subproblem 1
r + -1.75 = 1.030776406 Simplifying r + -1.75 = 1.030776406 Reorder the terms: -1.75 + r = 1.030776406 Solving -1.75 + r = 1.030776406 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + r = 1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + r = 1.030776406 + 1.75 r = 1.030776406 + 1.75 Combine like terms: 1.030776406 + 1.75 = 2.780776406 r = 2.780776406 Simplifying r = 2.780776406Subproblem 2
r + -1.75 = -1.030776406 Simplifying r + -1.75 = -1.030776406 Reorder the terms: -1.75 + r = -1.030776406 Solving -1.75 + r = -1.030776406 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + r = -1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + r = -1.030776406 + 1.75 r = -1.030776406 + 1.75 Combine like terms: -1.030776406 + 1.75 = 0.719223594 r = 0.719223594 Simplifying r = 0.719223594Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.780776406, 0.719223594}
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