1.96=r^2+2r+1

Solution for 1.96=r^2+2r+1 equation:

Simplifying
1.96 = r2 + 2r + 1

Reorder the terms:
1.96 = 1 + 2r + r2

Solving
1.96 = 1 + 2r + r2

Solving for variable 'r'.

Combine like terms: 1.96 + -1 = 0.96
0.96 + -2r + -1r2 = 1 + 2r + r2 + -1 + -2r + -1r2

Reorder the terms:
0.96 + -2r + -1r2 = 1 + -1 + 2r + -2r + r2 + -1r2

Combine like terms: 1 + -1 = 0
0.96 + -2r + -1r2 = 0 + 2r + -2r + r2 + -1r2
0.96 + -2r + -1r2 = 2r + -2r + r2 + -1r2

Combine like terms: 2r + -2r = 0
0.96 + -2r + -1r2 = 0 + r2 + -1r2
0.96 + -2r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
0.96 + -2r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.96 + 2r + r2 = 0

Move the constant term to the right:

Add '0.96' to each side of the equation.
-0.96 + 2r + 0.96 + r2 = 0 + 0.96

Reorder the terms:
-0.96 + 0.96 + 2r + r2 = 0 + 0.96

Combine like terms: -0.96 + 0.96 = 0.00
0.00 + 2r + r2 = 0 + 0.96
2r + r2 = 0 + 0.96

Combine like terms: 0 + 0.96 = 0.96
2r + r2 = 0.96

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 = 0.96 + 1

Reorder the terms:
1 + 2r + r2 = 0.96 + 1

Combine like terms: 0.96 + 1 = 1.96
1 + 2r + r2 = 1.96

Factor a perfect square on the left side:
(r + 1)(r + 1) = 1.96

Calculate the square root of the right side: 1.4

Break this problem into two subproblems by setting 
(r + 1) equal to 1.4 and -1.4.

Subproblem 1
r + 1 = 1.4

Simplifying
r + 1 = 1.4

Reorder the terms:
1 + r = 1.4

Solving
1 + r = 1.4

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 = 1.4 + -1

Combine like terms: 1 + -1 = 0
0 + r = 1.4 + -1
r = 1.4 + -1

Combine like terms: 1.4 + -1 = 0.4
r = 0.4

Simplifying
r = 0.4

Subproblem 2
r + 1 = -1.4

Simplifying
r + 1 = -1.4

Reorder the terms:
1 + r = -1.4

Solving
1 + r = -1.4

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 = -1.4 + -1

Combine like terms: 1 + -1 = 0
0 + r = -1.4 + -1
r = -1.4 + -1

Combine like terms: -1.4 + -1 = -2.4
r = -2.4

Simplifying
r = -2.4

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.4, -2.4}