r^2-4r=-2

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Solution for r^2-4r=-2 equation: 


Simplifying
r2 + -4r = -2

Reorder the terms:
-4r + r2 = -2

Solving
-4r + r2 = -2

Solving for variable 'r'.

Reorder the terms:
2 + -4r + r2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4r + -2 + r2 = 0 + -2

Reorder the terms:
2 + -2 + -4r + r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4r + r2 = 0 + -2
-4r + r2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4r + r2 = -2

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = -2 + 4

Reorder the terms:
4 + -4r + r2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + -4r + r2 = 2

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

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(r + -2) equal to 1.414213562 and -1.414213562.


Subproblem 1
r + -2 = 1.414213562

Simplifying
r + -2 = 1.414213562

Reorder the terms:
-2 + r = 1.414213562

Solving
-2 + r = 1.414213562

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + r = 1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + r = 1.414213562 + 2
r = 1.414213562 + 2

Combine like terms: 1.414213562 + 2 = 3.414213562
r = 3.414213562

Simplifying
r = 3.414213562


Subproblem 2
r + -2 = -1.414213562

Simplifying
r + -2 = -1.414213562

Reorder the terms:
-2 + r = -1.414213562

Solving
-2 + r = -1.414213562

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + r = -1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + r = -1.414213562 + 2
r = -1.414213562 + 2

Combine like terms: -1.414213562 + 2 = 0.585786438
r = 0.585786438

Simplifying
r = 0.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.414213562, 0.585786438}

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