r^2-6r-71=0

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Solution for r^2-6r-71=0 equation:


Simplifying
r2 + -6r + -71 = 0

Reorder the terms:
-71 + -6r + r2 = 0

Solving
-71 + -6r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + -6r + 71 + r2 = 0 + 71

Reorder the terms:
-71 + 71 + -6r + r2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + -6r + r2 = 0 + 71
-6r + r2 = 0 + 71

Combine like terms: 0 + 71 = 71
-6r + r2 = 71

The r term is -6r.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6r + 9 + r2 = 71 + 9

Reorder the terms:
9 + -6r + r2 = 71 + 9

Combine like terms: 71 + 9 = 80
9 + -6r + r2 = 80

Factor a perfect square on the left side:
(r + -3)(r + -3) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(r + -3) equal to 8.94427191 and -8.94427191.

Subproblem 1

r + -3 = 8.94427191 Simplifying r + -3 = 8.94427191 Reorder the terms: -3 + r = 8.94427191 Solving -3 + r = 8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = 8.94427191 + 3 Combine like terms: -3 + 3 = 0 0 + r = 8.94427191 + 3 r = 8.94427191 + 3 Combine like terms: 8.94427191 + 3 = 11.94427191 r = 11.94427191 Simplifying r = 11.94427191

Subproblem 2

r + -3 = -8.94427191 Simplifying r + -3 = -8.94427191 Reorder the terms: -3 + r = -8.94427191 Solving -3 + r = -8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = -8.94427191 + 3 Combine like terms: -3 + 3 = 0 0 + r = -8.94427191 + 3 r = -8.94427191 + 3 Combine like terms: -8.94427191 + 3 = -5.94427191 r = -5.94427191 Simplifying r = -5.94427191

Solution

The solution to the problem is based on the solutions from the subproblems. r = {11.94427191, -5.94427191}

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