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Simplifying 36r2 + 36r + -120 = 0 Reorder the terms: -120 + 36r + 36r2 = 0 Solving -120 + 36r + 36r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '12'. 12(-10 + 3r + 3r2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-10 + 3r + 3r2)' equal to zero and attempt to solve: Simplifying -10 + 3r + 3r2 = 0 Solving -10 + 3r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + r + r2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + r + 3.333333333 + r2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + r + r2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + r + r2 = 0 + 3.333333333 r + r2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 r + r2 = 3.333333333 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + r2 = 3.333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + r2 = 3.333333333 + 0.25 Combine like terms: 3.333333333 + 0.25 = 3.583333333 1.25 + r2 = 3.583333333 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (r + 0.5) equal to 1.892969449 and -1.892969449.Subproblem 1
r + 0.5 = 1.892969449 Simplifying r + 0.5 = 1.892969449 Reorder the terms: 0.5 + r = 1.892969449 Solving 0.5 + r = 1.892969449 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 1.892969449 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 1.892969449 + -0.5 r = 1.892969449 + -0.5 Combine like terms: 1.892969449 + -0.5 = 1.392969449 r = 1.392969449 Simplifying r = 1.392969449Subproblem 2
r + 0.5 = -1.892969449 Simplifying r + 0.5 = -1.892969449 Reorder the terms: 0.5 + r = -1.892969449 Solving 0.5 + r = -1.892969449 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -1.892969449 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -1.892969449 + -0.5 r = -1.892969449 + -0.5 Combine like terms: -1.892969449 + -0.5 = -2.392969449 r = -2.392969449 Simplifying r = -2.392969449Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.392969449, -2.392969449}Solution
r = {1.392969449, -2.392969449}
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