r^2+4.3r-0.9=0

Solution for r^2+4.3r-0.9=0 equation:

Simplifying
r2 + 4.3r + -0.9 = 0

Reorder the terms:
-0.9 + 4.3r + r2 = 0

Solving
-0.9 + 4.3r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '0.9' to each side of the equation.
-0.9 + 4.3r + 0.9 + r2 = 0 + 0.9

Reorder the terms:
-0.9 + 0.9 + 4.3r + r2 = 0 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + 4.3r + r2 = 0 + 0.9
4.3r + r2 = 0 + 0.9

Combine like terms: 0 + 0.9 = 0.9
4.3r + r2 = 0.9

The r term is 4.3r.  Take half its coefficient (2.15).
Square it (4.6225) and add it to both sides.

Add '4.6225' to each side of the equation.
4.3r + 4.6225 + r2 = 0.9 + 4.6225

Reorder the terms:
4.6225 + 4.3r + r2 = 0.9 + 4.6225

Combine like terms: 0.9 + 4.6225 = 5.5225
4.6225 + 4.3r + r2 = 5.5225

Factor a perfect square on the left side:
(r + 2.15)(r + 2.15) = 5.5225

Calculate the square root of the right side: 2.35

Break this problem into two subproblems by setting 
(r + 2.15) equal to 2.35 and -2.35.

Subproblem 1
r + 2.15 = 2.35

Simplifying
r + 2.15 = 2.35

Reorder the terms:
2.15 + r = 2.35

Solving
2.15 + r = 2.35

Solving for variable 'r'.

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

Add '-2.15' to each side of the equation.
2.15 + -2.15 + r = 2.35 + -2.15

Combine like terms: 2.15 + -2.15 = 0.00
0.00 + r = 2.35 + -2.15
r = 2.35 + -2.15

Combine like terms: 2.35 + -2.15 = 0.2
r = 0.2

Simplifying
r = 0.2

Subproblem 2
r + 2.15 = -2.35

Simplifying
r + 2.15 = -2.35

Reorder the terms:
2.15 + r = -2.35

Solving
2.15 + r = -2.35

Solving for variable 'r'.

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

Add '-2.15' to each side of the equation.
2.15 + -2.15 + r = -2.35 + -2.15

Combine like terms: 2.15 + -2.15 = 0.00
0.00 + r = -2.35 + -2.15
r = -2.35 + -2.15

Combine like terms: -2.35 + -2.15 = -4.5
r = -4.5

Simplifying
r = -4.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.2, -4.5}