633.024=2(3.14)(r)(16.2)+2(3.14)(r*r)

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Solution for 633.024=2(3.14)(r)(16.2)+2(3.14)(r*r) equation: 


Simplifying
633.024 = 2(3.14)(r)(16.2) + 2(3.14)(r * r)

Reorder the terms for easier multiplication:
633.024 = 2 * 3.14 * 16.2r + 2(3.14)(r * r)

Multiply 2 * 3.14
633.024 = 6.28 * 16.2r + 2(3.14)(r * r)

Multiply 6.28 * 16.2
633.024 = 101.736r + 2(3.14)(r * r)

Multiply r * r
633.024 = 101.736r + 2 * 3.14(r2)

Multiply 2 * 3.14
633.024 = 101.736r + 6.28r2

Solving
633.024 = 101.736r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
633.024 + -101.736r + -6.28r2 = 101.736r + -101.736r + 6.28r2 + -6.28r2

Combine like terms: 101.736r + -101.736r = 0.000
633.024 + -101.736r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
633.024 + -101.736r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
633.024 + -101.736r + -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'.
-100.8 + 16.2r + r2 = 0

Move the constant term to the right:

Add '100.8' to each side of the equation.
-100.8 + 16.2r + 100.8 + r2 = 0 + 100.8

Reorder the terms:
-100.8 + 100.8 + 16.2r + r2 = 0 + 100.8

Combine like terms: -100.8 + 100.8 = 0.0
0.0 + 16.2r + r2 = 0 + 100.8
16.2r + r2 = 0 + 100.8

Combine like terms: 0 + 100.8 = 100.8
16.2r + r2 = 100.8

The r term is 16.2r.  Take half its coefficient (8.1).
Square it (65.61) and add it to both sides.

Add '65.61' to each side of the equation.
16.2r + 65.61 + r2 = 100.8 + 65.61

Reorder the terms:
65.61 + 16.2r + r2 = 100.8 + 65.61

Combine like terms: 100.8 + 65.61 = 166.41
65.61 + 16.2r + r2 = 166.41

Factor a perfect square on the left side:
(r + 8.1)(r + 8.1) = 166.41

Calculate the square root of the right side: 12.9

Break this problem into two subproblems by setting 
(r + 8.1) equal to 12.9 and -12.9.


Subproblem 1
r + 8.1 = 12.9

Simplifying
r + 8.1 = 12.9

Reorder the terms:
8.1 + r = 12.9

Solving
8.1 + r = 12.9

Solving for variable 'r'.

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

Add '-8.1' to each side of the equation.
8.1 + -8.1 + r = 12.9 + -8.1

Combine like terms: 8.1 + -8.1 = 0.0
0.0 + r = 12.9 + -8.1
r = 12.9 + -8.1

Combine like terms: 12.9 + -8.1 = 4.8
r = 4.8

Simplifying
r = 4.8


Subproblem 2
r + 8.1 = -12.9

Simplifying
r + 8.1 = -12.9

Reorder the terms:
8.1 + r = -12.9

Solving
8.1 + r = -12.9

Solving for variable 'r'.

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

Add '-8.1' to each side of the equation.
8.1 + -8.1 + r = -12.9 + -8.1

Combine like terms: 8.1 + -8.1 = 0.0
0.0 + r = -12.9 + -8.1
r = -12.9 + -8.1

Combine like terms: -12.9 + -8.1 = -21
r = -21

Simplifying
r = -21


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.8, -21}

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