49r^2+28r-4=0

Solution for 49r^2+28r-4=0 equation:

Simplifying
49r2 + 28r + -4 = 0

Reorder the terms:
-4 + 28r + 49r2 = 0

Solving
-4 + 28r + 49r2 = 0

Solving for variable 'r'.

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

Divide each side by '49'.
-0.08163265306 + 0.5714285714r + r2 = 0

Move the constant term to the right:

Add '0.08163265306' to each side of the equation.
-0.08163265306 + 0.5714285714r + 0.08163265306 + r2 = 0 + 0.08163265306

Reorder the terms:
-0.08163265306 + 0.08163265306 + 0.5714285714r + r2 = 0 + 0.08163265306

Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000
0.00000000000 + 0.5714285714r + r2 = 0 + 0.08163265306
0.5714285714r + r2 = 0 + 0.08163265306

Combine like terms: 0 + 0.08163265306 = 0.08163265306
0.5714285714r + r2 = 0.08163265306

The r term is 0.5714285714r.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714r + 0.08163265305 + r2 = 0.08163265306 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714r + r2 = 0.08163265306 + 0.08163265305

Combine like terms: 0.08163265306 + 0.08163265305 = 0.16326530611
0.08163265305 + 0.5714285714r + r2 = 0.16326530611

Factor a perfect square on the left side:
(r + 0.2857142857)(r + 0.2857142857) = 0.16326530611

Calculate the square root of the right side: 0.404061018

Break this problem into two subproblems by setting 
(r + 0.2857142857) equal to 0.404061018 and -0.404061018.

Subproblem 1
r + 0.2857142857 = 0.404061018

Simplifying
r + 0.2857142857 = 0.404061018

Reorder the terms:
0.2857142857 + r = 0.404061018

Solving
0.2857142857 + r = 0.404061018

Solving for variable 'r'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + r = 0.404061018 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + r = 0.404061018 + -0.2857142857
r = 0.404061018 + -0.2857142857

Combine like terms: 0.404061018 + -0.2857142857 = 0.1183467323
r = 0.1183467323

Simplifying
r = 0.1183467323

Subproblem 2
r + 0.2857142857 = -0.404061018

Simplifying
r + 0.2857142857 = -0.404061018

Reorder the terms:
0.2857142857 + r = -0.404061018

Solving
0.2857142857 + r = -0.404061018

Solving for variable 'r'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + r = -0.404061018 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + r = -0.404061018 + -0.2857142857
r = -0.404061018 + -0.2857142857

Combine like terms: -0.404061018 + -0.2857142857 = -0.6897753037
r = -0.6897753037

Simplifying
r = -0.6897753037

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.1183467323, -0.6897753037}