7r^2-14r=7

Solution for 7r^2-14r=7 equation:

Simplifying
7r2 + -14r = 7

Reorder the terms:
-14r + 7r2 = 7

Solving
-14r + 7r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + -14r + 7r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -14r + 7r2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-1 + -2r + r2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-1 + -2r + r2)' equal to zero and attempt to solve:

Simplifying
-1 + -2r + r2 = 0

Solving
-1 + -2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2r + 1 + r2 = 0 + 1

Reorder the terms:
-1 + 1 + -2r + r2 = 0 + 1

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

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

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 = 1 + 1

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

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

Factor a perfect square on the left side:
(r + -1)(r + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(r + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
r + -1 = 1.414213562

Simplifying
r + -1 = 1.414213562

Reorder the terms:
-1 + r = 1.414213562

Solving
-1 + r = 1.414213562

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 = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + r = 1.414213562 + 1
r = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
r = 2.414213562

Simplifying
r = 2.414213562

Subproblem 2
r + -1 = -1.414213562

Simplifying
r + -1 = -1.414213562

Reorder the terms:
-1 + r = -1.414213562

Solving
-1 + r = -1.414213562

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 = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + r = -1.414213562 + 1
r = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
r = -0.414213562

Simplifying
r = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.414213562, -0.414213562}
Solution
r = {2.414213562, -0.414213562}