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Simplifying r2 + -16r + 41 = 0 Reorder the terms: 41 + -16r + r2 = 0 Solving 41 + -16r + 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 + -16r + -41 + r2 = 0 + -41 Reorder the terms: 41 + -41 + -16r + r2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -16r + r2 = 0 + -41 -16r + r2 = 0 + -41 Combine like terms: 0 + -41 = -41 -16r + r2 = -41 The r term is -16r. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16r + 64 + r2 = -41 + 64 Reorder the terms: 64 + -16r + r2 = -41 + 64 Combine like terms: -41 + 64 = 23 64 + -16r + r2 = 23 Factor a perfect square on the left side: (r + -8)(r + -8) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (r + -8) equal to 4.795831523 and -4.795831523.Subproblem 1
r + -8 = 4.795831523 Simplifying r + -8 = 4.795831523 Reorder the terms: -8 + r = 4.795831523 Solving -8 + r = 4.795831523 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = 4.795831523 + 8 Combine like terms: -8 + 8 = 0 0 + r = 4.795831523 + 8 r = 4.795831523 + 8 Combine like terms: 4.795831523 + 8 = 12.795831523 r = 12.795831523 Simplifying r = 12.795831523Subproblem 2
r + -8 = -4.795831523 Simplifying r + -8 = -4.795831523 Reorder the terms: -8 + r = -4.795831523 Solving -8 + r = -4.795831523 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = -4.795831523 + 8 Combine like terms: -8 + 8 = 0 0 + r = -4.795831523 + 8 r = -4.795831523 + 8 Combine like terms: -4.795831523 + 8 = 3.204168477 r = 3.204168477 Simplifying r = 3.204168477Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.795831523, 3.204168477}
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