r^2-5r-2=0

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Solution for r^2-5r-2=0 equation: 


Simplifying
r2 + -5r + -2 = 0

Reorder the terms:
-2 + -5r + r2 = 0

Solving
-2 + -5r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -5r + 2 + r2 = 0 + 2

Reorder the terms:
-2 + 2 + -5r + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5r + r2 = 0 + 2
-5r + r2 = 0 + 2

Combine like terms: 0 + 2 = 2
-5r + r2 = 2

The r term is -5r.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5r + 6.25 + r2 = 2 + 6.25

Reorder the terms:
6.25 + -5r + r2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + -5r + r2 = 8.25

Factor a perfect square on the left side:
(r + -2.5)(r + -2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(r + -2.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
r + -2.5 = 2.872281323

Simplifying
r + -2.5 = 2.872281323

Reorder the terms:
-2.5 + r = 2.872281323

Solving
-2.5 + r = 2.872281323

Solving for variable 'r'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + r = 2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + r = 2.872281323 + 2.5
r = 2.872281323 + 2.5

Combine like terms: 2.872281323 + 2.5 = 5.372281323
r = 5.372281323

Simplifying
r = 5.372281323


Subproblem 2
r + -2.5 = -2.872281323

Simplifying
r + -2.5 = -2.872281323

Reorder the terms:
-2.5 + r = -2.872281323

Solving
-2.5 + r = -2.872281323

Solving for variable 'r'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + r = -2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + r = -2.872281323 + 2.5
r = -2.872281323 + 2.5

Combine like terms: -2.872281323 + 2.5 = -0.372281323
r = -0.372281323

Simplifying
r = -0.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.372281323, -0.372281323}

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