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Simplifying 6r2 = 60r + -24 Reorder the terms: 6r2 = -24 + 60r Solving 6r2 = -24 + 60r Solving for variable 'r'. Reorder the terms: 24 + -60r + 6r2 = -24 + 60r + 24 + -60r Reorder the terms: 24 + -60r + 6r2 = -24 + 24 + 60r + -60r Combine like terms: -24 + 24 = 0 24 + -60r + 6r2 = 0 + 60r + -60r 24 + -60r + 6r2 = 60r + -60r Combine like terms: 60r + -60r = 0 24 + -60r + 6r2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(4 + -10r + r2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + -10r + r2)' equal to zero and attempt to solve: Simplifying 4 + -10r + r2 = 0 Solving 4 + -10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10r + -4 + r2 = 0 + -4 Reorder the terms: 4 + -4 + -10r + r2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10r + r2 = 0 + -4 -10r + r2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10r + r2 = -4 The r term is -10r. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10r + 25 + r2 = -4 + 25 Reorder the terms: 25 + -10r + r2 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + -10r + r2 = 21 Factor a perfect square on the left side: (r + -5)(r + -5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (r + -5) equal to 4.582575695 and -4.582575695.Subproblem 1
r + -5 = 4.582575695 Simplifying r + -5 = 4.582575695 Reorder the terms: -5 + r = 4.582575695 Solving -5 + r = 4.582575695 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + r = 4.582575695 + 5 r = 4.582575695 + 5 Combine like terms: 4.582575695 + 5 = 9.582575695 r = 9.582575695 Simplifying r = 9.582575695Subproblem 2
r + -5 = -4.582575695 Simplifying r + -5 = -4.582575695 Reorder the terms: -5 + r = -4.582575695 Solving -5 + r = -4.582575695 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + r = -4.582575695 + 5 r = -4.582575695 + 5 Combine like terms: -4.582575695 + 5 = 0.417424305 r = 0.417424305 Simplifying r = 0.417424305Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.582575695, 0.417424305}Solution
r = {9.582575695, 0.417424305}
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