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Simplifying r2 + 3r + -72 = 0 Reorder the terms: -72 + 3r + r2 = 0 Solving -72 + 3r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 3r + 72 + r2 = 0 + 72 Reorder the terms: -72 + 72 + 3r + r2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 3r + r2 = 0 + 72 3r + r2 = 0 + 72 Combine like terms: 0 + 72 = 72 3r + r2 = 72 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 = 72 + 2.25 Reorder the terms: 2.25 + 3r + r2 = 72 + 2.25 Combine like terms: 72 + 2.25 = 74.25 2.25 + 3r + r2 = 74.25 Factor a perfect square on the left side: (r + 1.5)(r + 1.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (r + 1.5) equal to 8.61684397 and -8.61684397.Subproblem 1
r + 1.5 = 8.61684397 Simplifying r + 1.5 = 8.61684397 Reorder the terms: 1.5 + r = 8.61684397 Solving 1.5 + r = 8.61684397 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 = 8.61684397 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = 8.61684397 + -1.5 r = 8.61684397 + -1.5 Combine like terms: 8.61684397 + -1.5 = 7.11684397 r = 7.11684397 Simplifying r = 7.11684397Subproblem 2
r + 1.5 = -8.61684397 Simplifying r + 1.5 = -8.61684397 Reorder the terms: 1.5 + r = -8.61684397 Solving 1.5 + r = -8.61684397 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 = -8.61684397 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = -8.61684397 + -1.5 r = -8.61684397 + -1.5 Combine like terms: -8.61684397 + -1.5 = -10.11684397 r = -10.11684397 Simplifying r = -10.11684397Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.11684397, -10.11684397}
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