4r^2+2=-8r

Solution for 4r^2+2=-8r equation:

Simplifying
4r2 + 2 = -8r

Reorder the terms:
2 + 4r2 = -8r

Solving
2 + 4r2 = -8r

Solving for variable 'r'.

Reorder the terms:
2 + 8r + 4r2 = -8r + 8r

Combine like terms: -8r + 8r = 0
2 + 8r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 4r + 2r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 4r + 2r2)' equal to zero and attempt to solve:

Simplifying
1 + 4r + 2r2 = 0

Solving
1 + 4r + 2r2 = 0

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

Divide each side by '2'.
0.5 + 2r + r2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2r + -0.5 + r2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2r + r2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2r + r2 = 0 + -0.5
2r + r2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2r + r2 = -0.5

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 = -0.5 + 1

Reorder the terms:
1 + 2r + r2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + 2r + r2 = 0.5

Factor a perfect square on the left side:
(r + 1)(r + 1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(r + 1) equal to 0.707106781 and -0.707106781.

Subproblem 1
r + 1 = 0.707106781

Simplifying
r + 1 = 0.707106781

Reorder the terms:
1 + r = 0.707106781

Solving
1 + r = 0.707106781

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 = 0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + r = 0.707106781 + -1
r = 0.707106781 + -1

Combine like terms: 0.707106781 + -1 = -0.292893219
r = -0.292893219

Simplifying
r = -0.292893219

Subproblem 2
r + 1 = -0.707106781

Simplifying
r + 1 = -0.707106781

Reorder the terms:
1 + r = -0.707106781

Solving
1 + r = -0.707106781

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 = -0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + r = -0.707106781 + -1
r = -0.707106781 + -1

Combine like terms: -0.707106781 + -1 = -1.707106781
r = -1.707106781

Simplifying
r = -1.707106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.292893219, -1.707106781}
Solution
r = {-0.292893219, -1.707106781}