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Simplifying 12r2 + -36r + -588 = 0 Reorder the terms: -588 + -36r + 12r2 = 0 Solving -588 + -36r + 12r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '12'. 12(-49 + -3r + r2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-49 + -3r + r2)' equal to zero and attempt to solve: Simplifying -49 + -3r + r2 = 0 Solving -49 + -3r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -3r + 49 + r2 = 0 + 49 Reorder the terms: -49 + 49 + -3r + r2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -3r + r2 = 0 + 49 -3r + r2 = 0 + 49 Combine like terms: 0 + 49 = 49 -3r + r2 = 49 The r term is -3r. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3r + 2.25 + r2 = 49 + 2.25 Reorder the terms: 2.25 + -3r + r2 = 49 + 2.25 Combine like terms: 49 + 2.25 = 51.25 2.25 + -3r + r2 = 51.25 Factor a perfect square on the left side: (r + -1.5)(r + -1.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (r + -1.5) equal to 7.158910532 and -7.158910532.Subproblem 1
r + -1.5 = 7.158910532 Simplifying r + -1.5 = 7.158910532 Reorder the terms: -1.5 + r = 7.158910532 Solving -1.5 + r = 7.158910532 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = 7.158910532 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = 7.158910532 + 1.5 r = 7.158910532 + 1.5 Combine like terms: 7.158910532 + 1.5 = 8.658910532 r = 8.658910532 Simplifying r = 8.658910532Subproblem 2
r + -1.5 = -7.158910532 Simplifying r + -1.5 = -7.158910532 Reorder the terms: -1.5 + r = -7.158910532 Solving -1.5 + r = -7.158910532 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + r = -7.158910532 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + r = -7.158910532 + 1.5 r = -7.158910532 + 1.5 Combine like terms: -7.158910532 + 1.5 = -5.658910532 r = -5.658910532 Simplifying r = -5.658910532Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.658910532, -5.658910532}Solution
r = {8.658910532, -5.658910532}
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