2458.2432=2*3.14*r^2+2*3.14*r*99.7

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Solution for 2458.2432=2*3.14*r^2+2*3.14*r*99.7 equation: 


Simplifying
2458.2432 = 2 * 3.14r2 + 2 * 3.14r * 99.7

Multiply 2 * 3.14
2458.2432 = 6.28r2 + 2 * 3.14r * 99.7

Reorder the terms for easier multiplication:
2458.2432 = 6.28r2 + 2 * 3.14 * 99.7r

Multiply 2 * 3.14
2458.2432 = 6.28r2 + 6.28 * 99.7r

Multiply 6.28 * 99.7
2458.2432 = 6.28r2 + 626.116r

Reorder the terms:
2458.2432 = 626.116r + 6.28r2

Solving
2458.2432 = 626.116r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
2458.2432 + -626.116r + -6.28r2 = 626.116r + -626.116r + 6.28r2 + -6.28r2

Combine like terms: 626.116r + -626.116r = 0.000
2458.2432 + -626.116r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
2458.2432 + -626.116r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
2458.2432 + -626.116r + -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'.
-391.44 + 99.7r + r2 = 0

Move the constant term to the right:

Add '391.44' to each side of the equation.
-391.44 + 99.7r + 391.44 + r2 = 0 + 391.44

Reorder the terms:
-391.44 + 391.44 + 99.7r + r2 = 0 + 391.44

Combine like terms: -391.44 + 391.44 = 0.00
0.00 + 99.7r + r2 = 0 + 391.44
99.7r + r2 = 0 + 391.44

Combine like terms: 0 + 391.44 = 391.44
99.7r + r2 = 391.44

The r term is 99.7r.  Take half its coefficient (49.85).
Square it (2485.0225) and add it to both sides.

Add '2485.0225' to each side of the equation.
99.7r + 2485.0225 + r2 = 391.44 + 2485.0225

Reorder the terms:
2485.0225 + 99.7r + r2 = 391.44 + 2485.0225

Combine like terms: 391.44 + 2485.0225 = 2876.4625
2485.0225 + 99.7r + r2 = 2876.4625

Factor a perfect square on the left side:
(r + 49.85)(r + 49.85) = 2876.4625

Calculate the square root of the right side: 53.632662623

Break this problem into two subproblems by setting 
(r + 49.85) equal to 53.632662623 and -53.632662623.


Subproblem 1
r + 49.85 = 53.632662623

Simplifying
r + 49.85 = 53.632662623

Reorder the terms:
49.85 + r = 53.632662623

Solving
49.85 + r = 53.632662623

Solving for variable 'r'.

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

Add '-49.85' to each side of the equation.
49.85 + -49.85 + r = 53.632662623 + -49.85

Combine like terms: 49.85 + -49.85 = 0.00
0.00 + r = 53.632662623 + -49.85
r = 53.632662623 + -49.85

Combine like terms: 53.632662623 + -49.85 = 3.782662623
r = 3.782662623

Simplifying
r = 3.782662623


Subproblem 2
r + 49.85 = -53.632662623

Simplifying
r + 49.85 = -53.632662623

Reorder the terms:
49.85 + r = -53.632662623

Solving
49.85 + r = -53.632662623

Solving for variable 'r'.

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

Add '-49.85' to each side of the equation.
49.85 + -49.85 + r = -53.632662623 + -49.85

Combine like terms: 49.85 + -49.85 = 0.00
0.00 + r = -53.632662623 + -49.85
r = -53.632662623 + -49.85

Combine like terms: -53.632662623 + -49.85 = -103.482662623
r = -103.482662623

Simplifying
r = -103.482662623


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.782662623, -103.482662623}

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