7r^2-5r-10=0

Solution for 7r^2-5r-10=0 equation:

Simplifying
7r2 + -5r + -10 = 0

Reorder the terms:
-10 + -5r + 7r2 = 0

Solving
-10 + -5r + 7r2 = 0

Solving for variable 'r'.

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

Divide each side by '7'.
-1.428571429 + -0.7142857143r + r2 = 0

Move the constant term to the right:

Add '1.428571429' to each side of the equation.
-1.428571429 + -0.7142857143r + 1.428571429 + r2 = 0 + 1.428571429

Reorder the terms:
-1.428571429 + 1.428571429 + -0.7142857143r + r2 = 0 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + -0.7142857143r + r2 = 0 + 1.428571429
-0.7142857143r + r2 = 0 + 1.428571429

Combine like terms: 0 + 1.428571429 = 1.428571429
-0.7142857143r + r2 = 1.428571429

The r term is -0.7142857143r.  Take half its coefficient (-0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
-0.7142857143r + 0.1275510204 + r2 = 1.428571429 + 0.1275510204

Reorder the terms:
0.1275510204 + -0.7142857143r + r2 = 1.428571429 + 0.1275510204

Combine like terms: 1.428571429 + 0.1275510204 = 1.5561224494
0.1275510204 + -0.7142857143r + r2 = 1.5561224494

Factor a perfect square on the left side:
(r + -0.3571428572)(r + -0.3571428572) = 1.5561224494

Calculate the square root of the right side: 1.247446371

Break this problem into two subproblems by setting 
(r + -0.3571428572) equal to 1.247446371 and -1.247446371.

Subproblem 1
r + -0.3571428572 = 1.247446371

Simplifying
r + -0.3571428572 = 1.247446371

Reorder the terms:
-0.3571428572 + r = 1.247446371

Solving
-0.3571428572 + r = 1.247446371

Solving for variable 'r'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + r = 1.247446371 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + r = 1.247446371 + 0.3571428572
r = 1.247446371 + 0.3571428572

Combine like terms: 1.247446371 + 0.3571428572 = 1.6045892282
r = 1.6045892282

Simplifying
r = 1.6045892282

Subproblem 2
r + -0.3571428572 = -1.247446371

Simplifying
r + -0.3571428572 = -1.247446371

Reorder the terms:
-0.3571428572 + r = -1.247446371

Solving
-0.3571428572 + r = -1.247446371

Solving for variable 'r'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + r = -1.247446371 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + r = -1.247446371 + 0.3571428572
r = -1.247446371 + 0.3571428572

Combine like terms: -1.247446371 + 0.3571428572 = -0.8903035138
r = -0.8903035138

Simplifying
r = -0.8903035138

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.6045892282, -0.8903035138}