5r^2-44r+102=-30+11r

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Solution for 5r^2-44r+102=-30+11r equation:


Simplifying
5r2 + -44r + 102 = -30 + 11r

Reorder the terms:
102 + -44r + 5r2 = -30 + 11r

Solving
102 + -44r + 5r2 = -30 + 11r

Solving for variable 'r'.

Reorder the terms:
102 + 30 + -44r + -11r + 5r2 = -30 + 11r + 30 + -11r

Combine like terms: 102 + 30 = 132
132 + -44r + -11r + 5r2 = -30 + 11r + 30 + -11r

Combine like terms: -44r + -11r = -55r
132 + -55r + 5r2 = -30 + 11r + 30 + -11r

Reorder the terms:
132 + -55r + 5r2 = -30 + 30 + 11r + -11r

Combine like terms: -30 + 30 = 0
132 + -55r + 5r2 = 0 + 11r + -11r
132 + -55r + 5r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
132 + -55r + 5r2 = 0

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

Divide each side by '5'.
26.4 + -11r + r2 = 0

Move the constant term to the right:

Add '-26.4' to each side of the equation.
26.4 + -11r + -26.4 + r2 = 0 + -26.4

Reorder the terms:
26.4 + -26.4 + -11r + r2 = 0 + -26.4

Combine like terms: 26.4 + -26.4 = 0.0
0.0 + -11r + r2 = 0 + -26.4
-11r + r2 = 0 + -26.4

Combine like terms: 0 + -26.4 = -26.4
-11r + r2 = -26.4

The r term is -11r.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11r + 30.25 + r2 = -26.4 + 30.25

Reorder the terms:
30.25 + -11r + r2 = -26.4 + 30.25

Combine like terms: -26.4 + 30.25 = 3.85
30.25 + -11r + r2 = 3.85

Factor a perfect square on the left side:
(r + -5.5)(r + -5.5) = 3.85

Calculate the square root of the right side: 1.962141687

Break this problem into two subproblems by setting 
(r + -5.5) equal to 1.962141687 and -1.962141687.

Subproblem 1

r + -5.5 = 1.962141687 Simplifying r + -5.5 = 1.962141687 Reorder the terms: -5.5 + r = 1.962141687 Solving -5.5 + r = 1.962141687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = 1.962141687 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = 1.962141687 + 5.5 r = 1.962141687 + 5.5 Combine like terms: 1.962141687 + 5.5 = 7.462141687 r = 7.462141687 Simplifying r = 7.462141687

Subproblem 2

r + -5.5 = -1.962141687 Simplifying r + -5.5 = -1.962141687 Reorder the terms: -5.5 + r = -1.962141687 Solving -5.5 + r = -1.962141687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = -1.962141687 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = -1.962141687 + 5.5 r = -1.962141687 + 5.5 Combine like terms: -1.962141687 + 5.5 = 3.537858313 r = 3.537858313 Simplifying r = 3.537858313

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.462141687, 3.537858313}

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