r^2+4r-36=0

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Solution for r^2+4r-36=0 equation: 


Simplifying
r2 + 4r + -36 = 0

Reorder the terms:
-36 + 4r + r2 = 0

Solving
-36 + 4r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 4r + 36 + r2 = 0 + 36

Reorder the terms:
-36 + 36 + 4r + r2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 4r + r2 = 0 + 36
4r + r2 = 0 + 36

Combine like terms: 0 + 36 = 36
4r + r2 = 36

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = 36 + 4

Reorder the terms:
4 + 4r + r2 = 36 + 4

Combine like terms: 36 + 4 = 40
4 + 4r + r2 = 40

Factor a perfect square on the left side:
(r + 2)(r + 2) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(r + 2) equal to 6.32455532 and -6.32455532.


Subproblem 1
r + 2 = 6.32455532

Simplifying
r + 2 = 6.32455532

Reorder the terms:
2 + r = 6.32455532

Solving
2 + r = 6.32455532

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = 6.32455532 + -2

Combine like terms: 2 + -2 = 0
0 + r = 6.32455532 + -2
r = 6.32455532 + -2

Combine like terms: 6.32455532 + -2 = 4.32455532
r = 4.32455532

Simplifying
r = 4.32455532


Subproblem 2
r + 2 = -6.32455532

Simplifying
r + 2 = -6.32455532

Reorder the terms:
2 + r = -6.32455532

Solving
2 + r = -6.32455532

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = -6.32455532 + -2

Combine like terms: 2 + -2 = 0
0 + r = -6.32455532 + -2
r = -6.32455532 + -2

Combine like terms: -6.32455532 + -2 = -8.32455532
r = -8.32455532

Simplifying
r = -8.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.32455532, -8.32455532}

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