r^2+10r-60=0

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Solution for r^2+10r-60=0 equation: 


Simplifying
r2 + 10r + -60 = 0

Reorder the terms:
-60 + 10r + r2 = 0

Solving
-60 + 10r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 10r + 60 + r2 = 0 + 60

Reorder the terms:
-60 + 60 + 10r + r2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 10r + r2 = 0 + 60
10r + r2 = 0 + 60

Combine like terms: 0 + 60 = 60
10r + r2 = 60

The r term is 10r.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10r + 25 + r2 = 60 + 25

Reorder the terms:
25 + 10r + r2 = 60 + 25

Combine like terms: 60 + 25 = 85
25 + 10r + r2 = 85

Factor a perfect square on the left side:
(r + 5)(r + 5) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(r + 5) equal to 9.219544457 and -9.219544457.


Subproblem 1
r + 5 = 9.219544457

Simplifying
r + 5 = 9.219544457

Reorder the terms:
5 + r = 9.219544457

Solving
5 + r = 9.219544457

Solving for variable 'r'.

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

Add '-5' to each side of the equation.
5 + -5 + r = 9.219544457 + -5

Combine like terms: 5 + -5 = 0
0 + r = 9.219544457 + -5
r = 9.219544457 + -5

Combine like terms: 9.219544457 + -5 = 4.219544457
r = 4.219544457

Simplifying
r = 4.219544457


Subproblem 2
r + 5 = -9.219544457

Simplifying
r + 5 = -9.219544457

Reorder the terms:
5 + r = -9.219544457

Solving
5 + r = -9.219544457

Solving for variable 'r'.

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

Add '-5' to each side of the equation.
5 + -5 + r = -9.219544457 + -5

Combine like terms: 5 + -5 = 0
0 + r = -9.219544457 + -5
r = -9.219544457 + -5

Combine like terms: -9.219544457 + -5 = -14.219544457
r = -14.219544457

Simplifying
r = -14.219544457


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.219544457, -14.219544457}

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