r^2-5r=10

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Solution for r^2-5r=10 equation: 


Simplifying
r2 + -5r = 10

Reorder the terms:
-5r + r2 = 10

Solving
-5r + r2 = 10

Solving for variable 'r'.

Reorder the terms:
-10 + -5r + r2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -5r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -5r + 10 + r2 = 0 + 10

Reorder the terms:
-10 + 10 + -5r + r2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -5r + r2 = 0 + 10
-5r + r2 = 0 + 10

Combine like terms: 0 + 10 = 10
-5r + r2 = 10

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 = 10 + 6.25

Reorder the terms:
6.25 + -5r + r2 = 10 + 6.25

Combine like terms: 10 + 6.25 = 16.25
6.25 + -5r + r2 = 16.25

Factor a perfect square on the left side:
(r + -2.5)(r + -2.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(r + -2.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
r + -2.5 = 4.031128874

Simplifying
r + -2.5 = 4.031128874

Reorder the terms:
-2.5 + r = 4.031128874

Solving
-2.5 + r = 4.031128874

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 = 4.031128874 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + r = 4.031128874 + 2.5
r = 4.031128874 + 2.5

Combine like terms: 4.031128874 + 2.5 = 6.531128874
r = 6.531128874

Simplifying
r = 6.531128874


Subproblem 2
r + -2.5 = -4.031128874

Simplifying
r + -2.5 = -4.031128874

Reorder the terms:
-2.5 + r = -4.031128874

Solving
-2.5 + r = -4.031128874

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 = -4.031128874 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + r = -4.031128874 + 2.5
r = -4.031128874 + 2.5

Combine like terms: -4.031128874 + 2.5 = -1.531128874
r = -1.531128874

Simplifying
r = -1.531128874


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.531128874, -1.531128874}

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