r^2+4r-4=0

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Solution for r^2+4r-4=0 equation: 


Simplifying
r2 + 4r + -4 = 0

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

Solving
-4 + 4r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + 4r + r2 = 8

Factor a perfect square on the left side:
(r + 2)(r + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(r + 2) equal to 2.828427125 and -2.828427125.


Subproblem 1
r + 2 = 2.828427125

Simplifying
r + 2 = 2.828427125

Reorder the terms:
2 + r = 2.828427125

Solving
2 + r = 2.828427125

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 = 2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + r = 2.828427125 + -2
r = 2.828427125 + -2

Combine like terms: 2.828427125 + -2 = 0.828427125
r = 0.828427125

Simplifying
r = 0.828427125


Subproblem 2
r + 2 = -2.828427125

Simplifying
r + 2 = -2.828427125

Reorder the terms:
2 + r = -2.828427125

Solving
2 + r = -2.828427125

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 = -2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + r = -2.828427125 + -2
r = -2.828427125 + -2

Combine like terms: -2.828427125 + -2 = -4.828427125
r = -4.828427125

Simplifying
r = -4.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.828427125, -4.828427125}

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