r^2+2r=0.4

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Solution for r^2+2r=0.4 equation: 


Simplifying
r2 + 2r = 0.4

Reorder the terms:
2r + r2 = 0.4

Solving
2r + r2 = 0.4

Solving for variable 'r'.

Reorder the terms:
-0.4 + 2r + r2 = 0.4 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
-0.4 + 2r + r2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 2r + 0.4 + r2 = 0.0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 2r + r2 = 0.0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 2r + r2 = 0.0 + 0.4
2r + r2 = 0.0 + 0.4

Combine like terms: 0.0 + 0.4 = 0.4
2r + r2 = 0.4

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 0.4 + 1

Reorder the terms:
1 + 2r + r2 = 0.4 + 1

Combine like terms: 0.4 + 1 = 1.4
1 + 2r + r2 = 1.4

Factor a perfect square on the left side:
(r + 1)(r + 1) = 1.4

Calculate the square root of the right side: 1.183215957

Break this problem into two subproblems by setting 
(r + 1) equal to 1.183215957 and -1.183215957.


Subproblem 1
r + 1 = 1.183215957

Simplifying
r + 1 = 1.183215957

Reorder the terms:
1 + r = 1.183215957

Solving
1 + r = 1.183215957

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = 1.183215957 + -1

Combine like terms: 1 + -1 = 0
0 + r = 1.183215957 + -1
r = 1.183215957 + -1

Combine like terms: 1.183215957 + -1 = 0.183215957
r = 0.183215957

Simplifying
r = 0.183215957


Subproblem 2
r + 1 = -1.183215957

Simplifying
r + 1 = -1.183215957

Reorder the terms:
1 + r = -1.183215957

Solving
1 + r = -1.183215957

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = -1.183215957 + -1

Combine like terms: 1 + -1 = 0
0 + r = -1.183215957 + -1
r = -1.183215957 + -1

Combine like terms: -1.183215957 + -1 = -2.183215957
r = -2.183215957

Simplifying
r = -2.183215957


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.183215957, -2.183215957}

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