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Simplifying r2 + 9r + -84 = 0 Reorder the terms: -84 + 9r + r2 = 0 Solving -84 + 9r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 9r + 84 + r2 = 0 + 84 Reorder the terms: -84 + 84 + 9r + r2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 9r + r2 = 0 + 84 9r + r2 = 0 + 84 Combine like terms: 0 + 84 = 84 9r + r2 = 84 The r term is 9r. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9r + 20.25 + r2 = 84 + 20.25 Reorder the terms: 20.25 + 9r + r2 = 84 + 20.25 Combine like terms: 84 + 20.25 = 104.25 20.25 + 9r + r2 = 104.25 Factor a perfect square on the left side: (r + 4.5)(r + 4.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (r + 4.5) equal to 10.210288928 and -10.210288928.Subproblem 1
r + 4.5 = 10.210288928 Simplifying r + 4.5 = 10.210288928 Reorder the terms: 4.5 + r = 10.210288928 Solving 4.5 + r = 10.210288928 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + r = 10.210288928 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = 10.210288928 + -4.5 r = 10.210288928 + -4.5 Combine like terms: 10.210288928 + -4.5 = 5.710288928 r = 5.710288928 Simplifying r = 5.710288928Subproblem 2
r + 4.5 = -10.210288928 Simplifying r + 4.5 = -10.210288928 Reorder the terms: 4.5 + r = -10.210288928 Solving 4.5 + r = -10.210288928 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + r = -10.210288928 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = -10.210288928 + -4.5 r = -10.210288928 + -4.5 Combine like terms: -10.210288928 + -4.5 = -14.710288928 r = -14.710288928 Simplifying r = -14.710288928Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.710288928, -14.710288928}
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