r^2+4r-3=0

Solution for r^2+4r-3=0 equation:

Simplifying
r2 + 4r + -3 = 0

Reorder the terms:
-3 + 4r + r2 = 0

Solving
-3 + 4r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 4r + 3 + r2 = 0 + 3

Reorder the terms:
-3 + 3 + 4r + r2 = 0 + 3

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

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

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = 3 + 4

Reorder the terms:
4 + 4r + r2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + 4r + r2 = 7

Factor a perfect square on the left side:
(r + 2)(r + 2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(r + 2) equal to 2.645751311 and -2.645751311.

Subproblem 1
r + 2 = 2.645751311

Simplifying
r + 2 = 2.645751311

Reorder the terms:
2 + r = 2.645751311

Solving
2 + r = 2.645751311

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = 2.645751311 + -2

Combine like terms: 2 + -2 = 0
0 + r = 2.645751311 + -2
r = 2.645751311 + -2

Combine like terms: 2.645751311 + -2 = 0.645751311
r = 0.645751311

Simplifying
r = 0.645751311

Subproblem 2
r + 2 = -2.645751311

Simplifying
r + 2 = -2.645751311

Reorder the terms:
2 + r = -2.645751311

Solving
2 + r = -2.645751311

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = -2.645751311 + -2

Combine like terms: 2 + -2 = 0
0 + r = -2.645751311 + -2
r = -2.645751311 + -2

Combine like terms: -2.645751311 + -2 = -4.645751311
r = -4.645751311

Simplifying
r = -4.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.645751311, -4.645751311}