r^2=0-9r-10

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Solution for r^2=0-9r-10 equation: 


Simplifying
r2 = 0 + -9r + -10

Reorder the terms:
r2 = 0 + -10 + -9r

Combine like terms: 0 + -10 = -10
r2 = -10 + -9r

Solving
r2 = -10 + -9r

Solving for variable 'r'.

Reorder the terms:
10 + 9r + r2 = -10 + -9r + 10 + 9r

Reorder the terms:
10 + 9r + r2 = -10 + 10 + -9r + 9r

Combine like terms: -10 + 10 = 0
10 + 9r + r2 = 0 + -9r + 9r
10 + 9r + r2 = -9r + 9r

Combine like terms: -9r + 9r = 0
10 + 9r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 9r + -10 + r2 = 0 + -10

Reorder the terms:
10 + -10 + 9r + r2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 9r + r2 = 0 + -10
9r + r2 = 0 + -10

Combine like terms: 0 + -10 = -10
9r + r2 = -10

The r term is 9r.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9r + 20.25 + r2 = -10 + 20.25

Reorder the terms:
20.25 + 9r + r2 = -10 + 20.25

Combine like terms: -10 + 20.25 = 10.25
20.25 + 9r + r2 = 10.25

Factor a perfect square on the left side:
(r + 4.5)(r + 4.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(r + 4.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
r + 4.5 = 3.201562119

Simplifying
r + 4.5 = 3.201562119

Reorder the terms:
4.5 + r = 3.201562119

Solving
4.5 + r = 3.201562119

Solving for variable 'r'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + r = 3.201562119 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + r = 3.201562119 + -4.5
r = 3.201562119 + -4.5

Combine like terms: 3.201562119 + -4.5 = -1.298437881
r = -1.298437881

Simplifying
r = -1.298437881


Subproblem 2
r + 4.5 = -3.201562119

Simplifying
r + 4.5 = -3.201562119

Reorder the terms:
4.5 + r = -3.201562119

Solving
4.5 + r = -3.201562119

Solving for variable 'r'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + r = -3.201562119 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + r = -3.201562119 + -4.5
r = -3.201562119 + -4.5

Combine like terms: -3.201562119 + -4.5 = -7.701562119
r = -7.701562119

Simplifying
r = -7.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-1.298437881, -7.701562119}

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