r^2-8r+1=0

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Solution for r^2-8r+1=0 equation:


Simplifying
r2 + -8r + 1 = 0

Reorder the terms:
1 + -8r + r2 = 0

Solving
1 + -8r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -8r + -1 + r2 = 0 + -1

Reorder the terms:
1 + -1 + -8r + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8r + r2 = 0 + -1
-8r + r2 = 0 + -1

Combine like terms: 0 + -1 = -1
-8r + r2 = -1

The r term is -8r.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8r + 16 + r2 = -1 + 16

Reorder the terms:
16 + -8r + r2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + -8r + r2 = 15

Factor a perfect square on the left side:
(r + -4)(r + -4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(r + -4) equal to 3.872983346 and -3.872983346.

Subproblem 1

r + -4 = 3.872983346 Simplifying r + -4 = 3.872983346 Reorder the terms: -4 + r = 3.872983346 Solving -4 + r = 3.872983346 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + r = 3.872983346 + 4 r = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 r = 7.872983346 Simplifying r = 7.872983346

Subproblem 2

r + -4 = -3.872983346 Simplifying r + -4 = -3.872983346 Reorder the terms: -4 + r = -3.872983346 Solving -4 + r = -3.872983346 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + r = -3.872983346 + 4 r = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 r = 0.127016654 Simplifying r = 0.127016654

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.872983346, 0.127016654}

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