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Simplifying r2 + 3r + -112 = 0 Reorder the terms: -112 + 3r + r2 = 0 Solving -112 + 3r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + 3r + 112 + r2 = 0 + 112 Reorder the terms: -112 + 112 + 3r + r2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 3r + r2 = 0 + 112 3r + r2 = 0 + 112 Combine like terms: 0 + 112 = 112 3r + r2 = 112 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 = 112 + 2.25 Reorder the terms: 2.25 + 3r + r2 = 112 + 2.25 Combine like terms: 112 + 2.25 = 114.25 2.25 + 3r + r2 = 114.25 Factor a perfect square on the left side: (r + 1.5)(r + 1.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (r + 1.5) equal to 10.688779163 and -10.688779163.Subproblem 1
r + 1.5 = 10.688779163 Simplifying r + 1.5 = 10.688779163 Reorder the terms: 1.5 + r = 10.688779163 Solving 1.5 + r = 10.688779163 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 = 10.688779163 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = 10.688779163 + -1.5 r = 10.688779163 + -1.5 Combine like terms: 10.688779163 + -1.5 = 9.188779163 r = 9.188779163 Simplifying r = 9.188779163Subproblem 2
r + 1.5 = -10.688779163 Simplifying r + 1.5 = -10.688779163 Reorder the terms: 1.5 + r = -10.688779163 Solving 1.5 + r = -10.688779163 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 = -10.688779163 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = -10.688779163 + -1.5 r = -10.688779163 + -1.5 Combine like terms: -10.688779163 + -1.5 = -12.188779163 r = -12.188779163 Simplifying r = -12.188779163Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.188779163, -12.188779163}
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