(6r^2-3r)-(8r+4)=

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Solution for (6r^2-3r)-(8r+4)= equation:


Simplifying
(6r2 + -3r) + -1(8r + 4) = 0

Reorder the terms:
(-3r + 6r2) + -1(8r + 4) = 0

Remove parenthesis around (-3r + 6r2)
-3r + 6r2 + -1(8r + 4) = 0

Reorder the terms:
-3r + 6r2 + -1(4 + 8r) = 0
-3r + 6r2 + (4 * -1 + 8r * -1) = 0
-3r + 6r2 + (-4 + -8r) = 0

Reorder the terms:
-4 + -3r + -8r + 6r2 = 0

Combine like terms: -3r + -8r = -11r
-4 + -11r + 6r2 = 0

Solving
-4 + -11r + 6r2 = 0

Solving for variable 'r'.

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

Divide each side by '6'.
-0.6666666667 + -1.833333333r + r2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -1.833333333r + 0.6666666667 + r2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -1.833333333r + r2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -1.833333333r + r2 = 0 + 0.6666666667
-1.833333333r + r2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-1.833333333r + r2 = 0.6666666667

The r term is -1.833333333r.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333r + 0.8402777775 + r2 = 0.6666666667 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333r + r2 = 0.6666666667 + 0.8402777775

Combine like terms: 0.6666666667 + 0.8402777775 = 1.5069444442
0.8402777775 + -1.833333333r + r2 = 1.5069444442

Factor a perfect square on the left side:
(r + -0.9166666665)(r + -0.9166666665) = 1.5069444442

Calculate the square root of the right side: 1.227576655

Break this problem into two subproblems by setting 
(r + -0.9166666665) equal to 1.227576655 and -1.227576655.

Subproblem 1

r + -0.9166666665 = 1.227576655 Simplifying r + -0.9166666665 = 1.227576655 Reorder the terms: -0.9166666665 + r = 1.227576655 Solving -0.9166666665 + r = 1.227576655 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + r = 1.227576655 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + r = 1.227576655 + 0.9166666665 r = 1.227576655 + 0.9166666665 Combine like terms: 1.227576655 + 0.9166666665 = 2.1442433215 r = 2.1442433215 Simplifying r = 2.1442433215

Subproblem 2

r + -0.9166666665 = -1.227576655 Simplifying r + -0.9166666665 = -1.227576655 Reorder the terms: -0.9166666665 + r = -1.227576655 Solving -0.9166666665 + r = -1.227576655 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + r = -1.227576655 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + r = -1.227576655 + 0.9166666665 r = -1.227576655 + 0.9166666665 Combine like terms: -1.227576655 + 0.9166666665 = -0.3109099885 r = -0.3109099885 Simplifying r = -0.3109099885

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.1442433215, -0.3109099885}

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