r^2-12r-4=10

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Solution for r^2-12r-4=10 equation: 


Simplifying
r2 + -12r + -4 = 10

Reorder the terms:
-4 + -12r + r2 = 10

Solving
-4 + -12r + r2 = 10

Solving for variable 'r'.

Reorder the terms:
-4 + -10 + -12r + r2 = 10 + -10

Combine like terms: -4 + -10 = -14
-14 + -12r + r2 = 10 + -10

Combine like terms: 10 + -10 = 0
-14 + -12r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -12r + 14 + r2 = 0 + 14

Reorder the terms:
-14 + 14 + -12r + r2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -12r + r2 = 0 + 14
-12r + r2 = 0 + 14

Combine like terms: 0 + 14 = 14
-12r + r2 = 14

The r term is -12r.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12r + 36 + r2 = 14 + 36

Reorder the terms:
36 + -12r + r2 = 14 + 36

Combine like terms: 14 + 36 = 50
36 + -12r + r2 = 50

Factor a perfect square on the left side:
(r + -6)(r + -6) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(r + -6) equal to 7.071067812 and -7.071067812.


Subproblem 1
r + -6 = 7.071067812

Simplifying
r + -6 = 7.071067812

Reorder the terms:
-6 + r = 7.071067812

Solving
-6 + r = 7.071067812

Solving for variable 'r'.

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

Add '6' to each side of the equation.
-6 + 6 + r = 7.071067812 + 6

Combine like terms: -6 + 6 = 0
0 + r = 7.071067812 + 6
r = 7.071067812 + 6

Combine like terms: 7.071067812 + 6 = 13.071067812
r = 13.071067812

Simplifying
r = 13.071067812


Subproblem 2
r + -6 = -7.071067812

Simplifying
r + -6 = -7.071067812

Reorder the terms:
-6 + r = -7.071067812

Solving
-6 + r = -7.071067812

Solving for variable 'r'.

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

Add '6' to each side of the equation.
-6 + 6 + r = -7.071067812 + 6

Combine like terms: -6 + 6 = 0
0 + r = -7.071067812 + 6
r = -7.071067812 + 6

Combine like terms: -7.071067812 + 6 = -1.071067812
r = -1.071067812

Simplifying
r = -1.071067812


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {13.071067812, -1.071067812}

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