11r^2-165r+5=0

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Solution for 11r^2-165r+5=0 equation:


Simplifying
11r2 + -165r + 5 = 0

Reorder the terms:
5 + -165r + 11r2 = 0

Solving
5 + -165r + 11r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
11 the coefficient of the squared term: 

Divide each side by '11'.
0.4545454545 + -15r + r2 = 0

Move the constant term to the right:

Add '-0.4545454545' to each side of the equation.
0.4545454545 + -15r + -0.4545454545 + r2 = 0 + -0.4545454545

Reorder the terms:
0.4545454545 + -0.4545454545 + -15r + r2 = 0 + -0.4545454545

Combine like terms: 0.4545454545 + -0.4545454545 = 0.0000000000
0.0000000000 + -15r + r2 = 0 + -0.4545454545
-15r + r2 = 0 + -0.4545454545

Combine like terms: 0 + -0.4545454545 = -0.4545454545
-15r + r2 = -0.4545454545

The r term is -15r.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15r + 56.25 + r2 = -0.4545454545 + 56.25

Reorder the terms:
56.25 + -15r + r2 = -0.4545454545 + 56.25

Combine like terms: -0.4545454545 + 56.25 = 55.7954545455
56.25 + -15r + r2 = 55.7954545455

Factor a perfect square on the left side:
(r + -7.5)(r + -7.5) = 55.7954545455

Calculate the square root of the right side: 7.469635503

Break this problem into two subproblems by setting 
(r + -7.5) equal to 7.469635503 and -7.469635503.

Subproblem 1

r + -7.5 = 7.469635503 Simplifying r + -7.5 = 7.469635503 Reorder the terms: -7.5 + r = 7.469635503 Solving -7.5 + r = 7.469635503 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + r = 7.469635503 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + r = 7.469635503 + 7.5 r = 7.469635503 + 7.5 Combine like terms: 7.469635503 + 7.5 = 14.969635503 r = 14.969635503 Simplifying r = 14.969635503

Subproblem 2

r + -7.5 = -7.469635503 Simplifying r + -7.5 = -7.469635503 Reorder the terms: -7.5 + r = -7.469635503 Solving -7.5 + r = -7.469635503 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + r = -7.469635503 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + r = -7.469635503 + 7.5 r = -7.469635503 + 7.5 Combine like terms: -7.469635503 + 7.5 = 0.030364497 r = 0.030364497 Simplifying r = 0.030364497

Solution

The solution to the problem is based on the solutions from the subproblems. r = {14.969635503, 0.030364497}

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