10r^2+4r=13

Solution for 10r^2+4r=13 equation:

Simplifying
10r2 + 4r = 13

Reorder the terms:
4r + 10r2 = 13

Solving
4r + 10r2 = 13

Solving for variable 'r'.

Reorder the terms:
-13 + 4r + 10r2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 4r + 10r2 = 0

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

Divide each side by '10'.
-1.3 + 0.4r + r2 = 0

Move the constant term to the right:

Add '1.3' to each side of the equation.
-1.3 + 0.4r + 1.3 + r2 = 0 + 1.3

Reorder the terms:
-1.3 + 1.3 + 0.4r + r2 = 0 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + 0.4r + r2 = 0 + 1.3
0.4r + r2 = 0 + 1.3

Combine like terms: 0 + 1.3 = 1.3
0.4r + r2 = 1.3

The r term is 0.4r.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4r + 0.04 + r2 = 1.3 + 0.04

Reorder the terms:
0.04 + 0.4r + r2 = 1.3 + 0.04

Combine like terms: 1.3 + 0.04 = 1.34
0.04 + 0.4r + r2 = 1.34

Factor a perfect square on the left side:
(r + 0.2)(r + 0.2) = 1.34

Calculate the square root of the right side: 1.15758369

Break this problem into two subproblems by setting 
(r + 0.2) equal to 1.15758369 and -1.15758369.

Subproblem 1
r + 0.2 = 1.15758369

Simplifying
r + 0.2 = 1.15758369

Reorder the terms:
0.2 + r = 1.15758369

Solving
0.2 + r = 1.15758369

Solving for variable 'r'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + r = 1.15758369 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + r = 1.15758369 + -0.2
r = 1.15758369 + -0.2

Combine like terms: 1.15758369 + -0.2 = 0.95758369
r = 0.95758369

Simplifying
r = 0.95758369

Subproblem 2
r + 0.2 = -1.15758369

Simplifying
r + 0.2 = -1.15758369

Reorder the terms:
0.2 + r = -1.15758369

Solving
0.2 + r = -1.15758369

Solving for variable 'r'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + r = -1.15758369 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + r = -1.15758369 + -0.2
r = -1.15758369 + -0.2

Combine like terms: -1.15758369 + -0.2 = -1.35758369
r = -1.35758369

Simplifying
r = -1.35758369

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.95758369, -1.35758369}