r^2+3r=1

Solution for r^2+3r=1 equation:

Simplifying
r2 + 3r = 1

Reorder the terms:
3r + r2 = 1

Solving
3r + r2 = 1

Solving for variable 'r'.

Reorder the terms:
-1 + 3r + r2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 3r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3r + 1 + r2 = 0 + 1

Reorder the terms:
-1 + 1 + 3r + r2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3r + r2 = 0 + 1
3r + r2 = 0 + 1

Combine like terms: 0 + 1 = 1
3r + r2 = 1

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 1 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + 3r + r2 = 3.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(r + 1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
r + 1.5 = 1.802775638

Simplifying
r + 1.5 = 1.802775638

Reorder the terms:
1.5 + r = 1.802775638

Solving
1.5 + r = 1.802775638

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = 1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = 1.802775638 + -1.5
r = 1.802775638 + -1.5

Combine like terms: 1.802775638 + -1.5 = 0.302775638
r = 0.302775638

Simplifying
r = 0.302775638

Subproblem 2
r + 1.5 = -1.802775638

Simplifying
r + 1.5 = -1.802775638

Reorder the terms:
1.5 + r = -1.802775638

Solving
1.5 + r = -1.802775638

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = -1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = -1.802775638 + -1.5
r = -1.802775638 + -1.5

Combine like terms: -1.802775638 + -1.5 = -3.302775638
r = -3.302775638

Simplifying
r = -3.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.302775638, -3.302775638}