756.74=6.28r^2+(6.28)r(19.1)

Solution for 756.74=6.28r^2+(6.28)r(19.1) equation:

Simplifying
756.74 = 6.28r2 + (6.28) * r(19.1)

Reorder the terms for easier multiplication:
756.74 = 6.28r2 + 6.28 * 19.1r

Multiply 6.28 * 19.1
756.74 = 6.28r2 + 119.948r

Reorder the terms:
756.74 = 119.948r + 6.28r2

Solving
756.74 = 119.948r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
756.74 + -119.948r + -6.28r2 = 119.948r + -119.948r + 6.28r2 + -6.28r2

Combine like terms: 119.948r + -119.948r = 0.000
756.74 + -119.948r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
756.74 + -119.948r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
756.74 + -119.948r + -6.28r2 = 0.00

Begin completing the square.  Divide all terms by
-6.28 the coefficient of the squared term: 

Divide each side by '-6.28'.
-120.5 + 19.1r + r2 = 0

Move the constant term to the right:

Add '120.5' to each side of the equation.
-120.5 + 19.1r + 120.5 + r2 = 0 + 120.5

Reorder the terms:
-120.5 + 120.5 + 19.1r + r2 = 0 + 120.5

Combine like terms: -120.5 + 120.5 = 0.0
0.0 + 19.1r + r2 = 0 + 120.5
19.1r + r2 = 0 + 120.5

Combine like terms: 0 + 120.5 = 120.5
19.1r + r2 = 120.5

The r term is 19.1r.  Take half its coefficient (9.55).
Square it (91.2025) and add it to both sides.

Add '91.2025' to each side of the equation.
19.1r + 91.2025 + r2 = 120.5 + 91.2025

Reorder the terms:
91.2025 + 19.1r + r2 = 120.5 + 91.2025

Combine like terms: 120.5 + 91.2025 = 211.7025
91.2025 + 19.1r + r2 = 211.7025

Factor a perfect square on the left side:
(r + 9.55)(r + 9.55) = 211.7025

Calculate the square root of the right side: 14.55

Break this problem into two subproblems by setting 
(r + 9.55) equal to 14.55 and -14.55.

Subproblem 1
r + 9.55 = 14.55

Simplifying
r + 9.55 = 14.55

Reorder the terms:
9.55 + r = 14.55

Solving
9.55 + r = 14.55

Solving for variable 'r'.

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

Add '-9.55' to each side of the equation.
9.55 + -9.55 + r = 14.55 + -9.55

Combine like terms: 9.55 + -9.55 = 0.00
0.00 + r = 14.55 + -9.55
r = 14.55 + -9.55

Combine like terms: 14.55 + -9.55 = 5
r = 5

Simplifying
r = 5

Subproblem 2
r + 9.55 = -14.55

Simplifying
r + 9.55 = -14.55

Reorder the terms:
9.55 + r = -14.55

Solving
9.55 + r = -14.55

Solving for variable 'r'.

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

Add '-9.55' to each side of the equation.
9.55 + -9.55 + r = -14.55 + -9.55

Combine like terms: 9.55 + -9.55 = 0.00
0.00 + r = -14.55 + -9.55
r = -14.55 + -9.55

Combine like terms: -14.55 + -9.55 = -24.1
r = -24.1

Simplifying
r = -24.1

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5, -24.1}