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Simplifying 7r2 + 60r = 32 Reorder the terms: 60r + 7r2 = 32 Solving 60r + 7r2 = 32 Solving for variable 'r'. Reorder the terms: -32 + 60r + 7r2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 60r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.571428571 + 8.571428571r + r2 = 0 Move the constant term to the right: Add '4.571428571' to each side of the equation. -4.571428571 + 8.571428571r + 4.571428571 + r2 = 0 + 4.571428571 Reorder the terms: -4.571428571 + 4.571428571 + 8.571428571r + r2 = 0 + 4.571428571 Combine like terms: -4.571428571 + 4.571428571 = 0.000000000 0.000000000 + 8.571428571r + r2 = 0 + 4.571428571 8.571428571r + r2 = 0 + 4.571428571 Combine like terms: 0 + 4.571428571 = 4.571428571 8.571428571r + r2 = 4.571428571 The r term is 8.571428571r. Take half its coefficient (4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. 8.571428571r + 18.36734694 + r2 = 4.571428571 + 18.36734694 Reorder the terms: 18.36734694 + 8.571428571r + r2 = 4.571428571 + 18.36734694 Combine like terms: 4.571428571 + 18.36734694 = 22.938775511 18.36734694 + 8.571428571r + r2 = 22.938775511 Factor a perfect square on the left side: (r + 4.285714286)(r + 4.285714286) = 22.938775511 Calculate the square root of the right side: 4.789444176 Break this problem into two subproblems by setting (r + 4.285714286) equal to 4.789444176 and -4.789444176.Subproblem 1
r + 4.285714286 = 4.789444176 Simplifying r + 4.285714286 = 4.789444176 Reorder the terms: 4.285714286 + r = 4.789444176 Solving 4.285714286 + r = 4.789444176 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + r = 4.789444176 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + r = 4.789444176 + -4.285714286 r = 4.789444176 + -4.285714286 Combine like terms: 4.789444176 + -4.285714286 = 0.50372989 r = 0.50372989 Simplifying r = 0.50372989Subproblem 2
r + 4.285714286 = -4.789444176 Simplifying r + 4.285714286 = -4.789444176 Reorder the terms: 4.285714286 + r = -4.789444176 Solving 4.285714286 + r = -4.789444176 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.285714286' to each side of the equation. 4.285714286 + -4.285714286 + r = -4.789444176 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + r = -4.789444176 + -4.285714286 r = -4.789444176 + -4.285714286 Combine like terms: -4.789444176 + -4.285714286 = -9.075158462 r = -9.075158462 Simplifying r = -9.075158462Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.50372989, -9.075158462}
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