r^2+17r+72.25=149.25

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Solution for r^2+17r+72.25=149.25 equation: 


Simplifying
r2 + 17r + 72.25 = 149.25

Reorder the terms:
72.25 + 17r + r2 = 149.25

Solving
72.25 + 17r + r2 = 149.25

Solving for variable 'r'.

Reorder the terms:
72.25 + -149.25 + 17r + r2 = 149.25 + -149.25

Combine like terms: 72.25 + -149.25 = -77
-77 + 17r + r2 = 149.25 + -149.25

Combine like terms: 149.25 + -149.25 = 0.00
-77 + 17r + r2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '77' to each side of the equation.
-77 + 17r + 77 + r2 = 0.00 + 77

Reorder the terms:
-77 + 77 + 17r + r2 = 0.00 + 77

Combine like terms: -77 + 77 = 0
0 + 17r + r2 = 0.00 + 77
17r + r2 = 0.00 + 77

Combine like terms: 0.00 + 77 = 77
17r + r2 = 77

The r term is 17r.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17r + 72.25 + r2 = 77 + 72.25

Reorder the terms:
72.25 + 17r + r2 = 77 + 72.25

Combine like terms: 77 + 72.25 = 149.25
72.25 + 17r + r2 = 149.25

Factor a perfect square on the left side:
(r + 8.5)(r + 8.5) = 149.25

Calculate the square root of the right side: 12.216791723

Break this problem into two subproblems by setting 
(r + 8.5) equal to 12.216791723 and -12.216791723.


Subproblem 1
r + 8.5 = 12.216791723

Simplifying
r + 8.5 = 12.216791723

Reorder the terms:
8.5 + r = 12.216791723

Solving
8.5 + r = 12.216791723

Solving for variable 'r'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + r = 12.216791723 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + r = 12.216791723 + -8.5
r = 12.216791723 + -8.5

Combine like terms: 12.216791723 + -8.5 = 3.716791723
r = 3.716791723

Simplifying
r = 3.716791723


Subproblem 2
r + 8.5 = -12.216791723

Simplifying
r + 8.5 = -12.216791723

Reorder the terms:
8.5 + r = -12.216791723

Solving
8.5 + r = -12.216791723

Solving for variable 'r'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + r = -12.216791723 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + r = -12.216791723 + -8.5
r = -12.216791723 + -8.5

Combine like terms: -12.216791723 + -8.5 = -20.716791723
r = -20.716791723

Simplifying
r = -20.716791723


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.716791723, -20.716791723}

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