2r^2-6r-8=3

Solution for 2r^2-6r-8=3 equation:

Simplifying
2r2 + -6r + -8 = 3

Reorder the terms:
-8 + -6r + 2r2 = 3

Solving
-8 + -6r + 2r2 = 3

Solving for variable 'r'.

Reorder the terms:
-8 + -3 + -6r + 2r2 = 3 + -3

Combine like terms: -8 + -3 = -11
-11 + -6r + 2r2 = 3 + -3

Combine like terms: 3 + -3 = 0
-11 + -6r + 2r2 = 0

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

Divide each side by '2'.
-5.5 + -3r + r2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -3r + 5.5 + r2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -3r + r2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -3r + r2 = 0 + 5.5
-3r + r2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-3r + r2 = 5.5

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 = 5.5 + 2.25

Reorder the terms:
2.25 + -3r + r2 = 5.5 + 2.25

Combine like terms: 5.5 + 2.25 = 7.75
2.25 + -3r + r2 = 7.75

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(r + -1.5) equal to 2.783882181 and -2.783882181.

Subproblem 1
r + -1.5 = 2.783882181

Simplifying
r + -1.5 = 2.783882181

Reorder the terms:
-1.5 + r = 2.783882181

Solving
-1.5 + r = 2.783882181

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 = 2.783882181 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = 2.783882181 + 1.5
r = 2.783882181 + 1.5

Combine like terms: 2.783882181 + 1.5 = 4.283882181
r = 4.283882181

Simplifying
r = 4.283882181

Subproblem 2
r + -1.5 = -2.783882181

Simplifying
r + -1.5 = -2.783882181

Reorder the terms:
-1.5 + r = -2.783882181

Solving
-1.5 + r = -2.783882181

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 = -2.783882181 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = -2.783882181 + 1.5
r = -2.783882181 + 1.5

Combine like terms: -2.783882181 + 1.5 = -1.283882181
r = -1.283882181

Simplifying
r = -1.283882181

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.283882181, -1.283882181}