r^2-8r+16=2

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Solution for r^2-8r+16=2 equation:


Simplifying
r2 + -8r + 16 = 2

Reorder the terms:
16 + -8r + r2 = 2

Solving
16 + -8r + r2 = 2

Solving for variable 'r'.

Reorder the terms:
16 + -2 + -8r + r2 = 2 + -2

Combine like terms: 16 + -2 = 14
14 + -8r + r2 = 2 + -2

Combine like terms: 2 + -2 = 0
14 + -8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -8r + -14 + r2 = 0 + -14

Reorder the terms:
14 + -14 + -8r + r2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -8r + r2 = 0 + -14
-8r + r2 = 0 + -14

Combine like terms: 0 + -14 = -14
-8r + r2 = -14

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 = -14 + 16

Reorder the terms:
16 + -8r + r2 = -14 + 16

Combine like terms: -14 + 16 = 2
16 + -8r + r2 = 2

Factor a perfect square on the left side:
(r + -4)(r + -4) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(r + -4) equal to 1.414213562 and -1.414213562.


Subproblem 1
r + -4 = 1.414213562

Simplifying
r + -4 = 1.414213562

Reorder the terms:
-4 + r = 1.414213562

Solving
-4 + r = 1.414213562

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 = 1.414213562 + 4

Combine like terms: -4 + 4 = 0
0 + r = 1.414213562 + 4
r = 1.414213562 + 4

Combine like terms: 1.414213562 + 4 = 5.414213562
r = 5.414213562

Simplifying
r = 5.414213562


Subproblem 2
r + -4 = -1.414213562

Simplifying
r + -4 = -1.414213562

Reorder the terms:
-4 + r = -1.414213562

Solving
-4 + r = -1.414213562

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 = -1.414213562 + 4

Combine like terms: -4 + 4 = 0
0 + r = -1.414213562 + 4
r = -1.414213562 + 4

Combine like terms: -1.414213562 + 4 = 2.585786438
r = 2.585786438

Simplifying
r = 2.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.414213562, 2.585786438}

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