r^2-16r+41=0

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Solution for r^2-16r+41=0 equation:


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 = 12.795831523

Subproblem 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 = 3.204168477

Solution

The solution to the problem is based on the solutions from the subproblems. r = {12.795831523, 3.204168477}

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