-r^2-17r-10=0

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Solution for -r^2-17r-10=0 equation: 


Simplifying
-1r2 + -17r + -10 = 0

Reorder the terms:
-10 + -17r + -1r2 = 0

Solving
-10 + -17r + -1r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 17r + r2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + 17r + r2)' equal to zero and attempt to solve:

Simplifying
10 + 17r + r2 = 0

Solving
10 + 17r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 17r + -10 + r2 = 0 + -10

Reorder the terms:
10 + -10 + 17r + r2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 17r + r2 = 0 + -10
17r + r2 = 0 + -10

Combine like terms: 0 + -10 = -10
17r + r2 = -10

The r term is 17r.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17r + 72.25 + r2 = -10 + 72.25

Reorder the terms:
72.25 + 17r + r2 = -10 + 72.25

Combine like terms: -10 + 72.25 = 62.25
72.25 + 17r + r2 = 62.25

Factor a perfect square on the left side:
(r + 8.5)(r + 8.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(r + 8.5) equal to 7.889866919 and -7.889866919.


Subproblem 1
r + 8.5 = 7.889866919

Simplifying
r + 8.5 = 7.889866919

Reorder the terms:
8.5 + r = 7.889866919

Solving
8.5 + r = 7.889866919

Solving for variable 'r'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + r = 7.889866919 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + r = 7.889866919 + -8.5
r = 7.889866919 + -8.5

Combine like terms: 7.889866919 + -8.5 = -0.610133081
r = -0.610133081

Simplifying
r = -0.610133081


Subproblem 2
r + 8.5 = -7.889866919

Simplifying
r + 8.5 = -7.889866919

Reorder the terms:
8.5 + r = -7.889866919

Solving
8.5 + r = -7.889866919

Solving for variable 'r'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + r = -7.889866919 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + r = -7.889866919 + -8.5
r = -7.889866919 + -8.5

Combine like terms: -7.889866919 + -8.5 = -16.389866919
r = -16.389866919

Simplifying
r = -16.389866919


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.610133081, -16.389866919}
Solution
r = {-0.610133081, -16.389866919}

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