r^2-12r-1=0

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Solution for r^2-12r-1=0 equation:


Simplifying
r2 + -12r + -1 = 0

Reorder the terms:
-1 + -12r + r2 = 0

Solving
-1 + -12r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -12r + 1 + r2 = 0 + 1

Reorder the terms:
-1 + 1 + -12r + r2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -12r + r2 = 0 + 1
-12r + r2 = 0 + 1

Combine like terms: 0 + 1 = 1
-12r + r2 = 1

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 = 1 + 36

Reorder the terms:
36 + -12r + r2 = 1 + 36

Combine like terms: 1 + 36 = 37
36 + -12r + r2 = 37

Factor a perfect square on the left side:
(r + -6)(r + -6) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(r + -6) equal to 6.08276253 and -6.08276253.

Subproblem 1

r + -6 = 6.08276253 Simplifying r + -6 = 6.08276253 Reorder the terms: -6 + r = 6.08276253 Solving -6 + r = 6.08276253 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 = 6.08276253 + 6 Combine like terms: -6 + 6 = 0 0 + r = 6.08276253 + 6 r = 6.08276253 + 6 Combine like terms: 6.08276253 + 6 = 12.08276253 r = 12.08276253 Simplifying r = 12.08276253

Subproblem 2

r + -6 = -6.08276253 Simplifying r + -6 = -6.08276253 Reorder the terms: -6 + r = -6.08276253 Solving -6 + r = -6.08276253 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 = -6.08276253 + 6 Combine like terms: -6 + 6 = 0 0 + r = -6.08276253 + 6 r = -6.08276253 + 6 Combine like terms: -6.08276253 + 6 = -0.08276253 r = -0.08276253 Simplifying r = -0.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. r = {12.08276253, -0.08276253}

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