r^2+4r+4=10

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Solution for r^2+4r+4=10 equation: 


Simplifying
r2 + 4r + 4 = 10

Reorder the terms:
4 + 4r + r2 = 10

Solving
4 + 4r + r2 = 10

Solving for variable 'r'.

Reorder the terms:
4 + -10 + 4r + r2 = 10 + -10

Combine like terms: 4 + -10 = -6
-6 + 4r + r2 = 10 + -10

Combine like terms: 10 + -10 = 0
-6 + 4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 4r + 6 + r2 = 0 + 6

Reorder the terms:
-6 + 6 + 4r + r2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 4r + r2 = 0 + 6
4r + r2 = 0 + 6

Combine like terms: 0 + 6 = 6
4r + r2 = 6

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 = 6 + 4

Reorder the terms:
4 + 4r + r2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + 4r + r2 = 10

Factor a perfect square on the left side:
(r + 2)(r + 2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(r + 2) equal to 3.16227766 and -3.16227766.


Subproblem 1
r + 2 = 3.16227766

Simplifying
r + 2 = 3.16227766

Reorder the terms:
2 + r = 3.16227766

Solving
2 + r = 3.16227766

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 = 3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + r = 3.16227766 + -2
r = 3.16227766 + -2

Combine like terms: 3.16227766 + -2 = 1.16227766
r = 1.16227766

Simplifying
r = 1.16227766


Subproblem 2
r + 2 = -3.16227766

Simplifying
r + 2 = -3.16227766

Reorder the terms:
2 + r = -3.16227766

Solving
2 + r = -3.16227766

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 = -3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + r = -3.16227766 + -2
r = -3.16227766 + -2

Combine like terms: -3.16227766 + -2 = -5.16227766
r = -5.16227766

Simplifying
r = -5.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.16227766, -5.16227766}

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