8r^2+4r+5=-3

Solution for 8r^2+4r+5=-3 equation:

Simplifying
8r2 + 4r + 5 = -3

Reorder the terms:
5 + 4r + 8r2 = -3

Solving
5 + 4r + 8r2 = -3

Solving for variable 'r'.

Reorder the terms:
5 + 3 + 4r + 8r2 = -3 + 3

Combine like terms: 5 + 3 = 8
8 + 4r + 8r2 = -3 + 3

Combine like terms: -3 + 3 = 0
8 + 4r + 8r2 = 0

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

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

Simplifying
2 + r + 2r2 = 0

Solving
2 + r + 2r2 = 0

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

Divide each side by '2'.
1 + 0.5r + r2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.5r + -1 + r2 = 0 + -1

Reorder the terms:
1 + -1 + 0.5r + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.5r + r2 = 0 + -1
0.5r + r2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.5r + r2 = -1

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5r + 0.25 + r2 = -1 + 0.25

Reorder the terms:
0.25 + 0.5r + r2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + 0.5r + r2 = -0.75

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.