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Simplifying r2 + 12r + -41 = 0 Reorder the terms: -41 + 12r + r2 = 0 Solving -41 + 12r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 12r + 41 + r2 = 0 + 41 Reorder the terms: -41 + 41 + 12r + r2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 12r + r2 = 0 + 41 12r + r2 = 0 + 41 Combine like terms: 0 + 41 = 41 12r + r2 = 41 The r term is 12r. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12r + 36 + r2 = 41 + 36 Reorder the terms: 36 + 12r + r2 = 41 + 36 Combine like terms: 41 + 36 = 77 36 + 12r + r2 = 77 Factor a perfect square on the left side: (r + 6)(r + 6) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (r + 6) equal to 8.774964387 and -8.774964387.Subproblem 1
r + 6 = 8.774964387 Simplifying r + 6 = 8.774964387 Reorder the terms: 6 + r = 8.774964387 Solving 6 + r = 8.774964387 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 8.774964387 + -6 Combine like terms: 6 + -6 = 0 0 + r = 8.774964387 + -6 r = 8.774964387 + -6 Combine like terms: 8.774964387 + -6 = 2.774964387 r = 2.774964387 Simplifying r = 2.774964387Subproblem 2
r + 6 = -8.774964387 Simplifying r + 6 = -8.774964387 Reorder the terms: 6 + r = -8.774964387 Solving 6 + r = -8.774964387 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -8.774964387 + -6 Combine like terms: 6 + -6 = 0 0 + r = -8.774964387 + -6 r = -8.774964387 + -6 Combine like terms: -8.774964387 + -6 = -14.774964387 r = -14.774964387 Simplifying r = -14.774964387Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.774964387, -14.774964387}
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