7r^2-28r-336=0

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Solution for 7r^2-28r-336=0 equation: 


Simplifying
7r2 + -28r + -336 = 0

Reorder the terms:
-336 + -28r + 7r2 = 0

Solving
-336 + -28r + 7r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-48 + -4r + r2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-48 + -4r + r2)' equal to zero and attempt to solve:

Simplifying
-48 + -4r + r2 = 0

Solving
-48 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -4r + 48 + r2 = 0 + 48

Reorder the terms:
-48 + 48 + -4r + r2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -4r + r2 = 0 + 48
-4r + r2 = 0 + 48

Combine like terms: 0 + 48 = 48
-4r + r2 = 48

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = 48 + 4

Reorder the terms:
4 + -4r + r2 = 48 + 4

Combine like terms: 48 + 4 = 52
4 + -4r + r2 = 52

Factor a perfect square on the left side:
(r + -2)(r + -2) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(r + -2) equal to 7.211102551 and -7.211102551.


Subproblem 1
r + -2 = 7.211102551

Simplifying
r + -2 = 7.211102551

Reorder the terms:
-2 + r = 7.211102551

Solving
-2 + r = 7.211102551

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + r = 7.211102551 + 2

Combine like terms: -2 + 2 = 0
0 + r = 7.211102551 + 2
r = 7.211102551 + 2

Combine like terms: 7.211102551 + 2 = 9.211102551
r = 9.211102551

Simplifying
r = 9.211102551


Subproblem 2
r + -2 = -7.211102551

Simplifying
r + -2 = -7.211102551

Reorder the terms:
-2 + r = -7.211102551

Solving
-2 + r = -7.211102551

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + r = -7.211102551 + 2

Combine like terms: -2 + 2 = 0
0 + r = -7.211102551 + 2
r = -7.211102551 + 2

Combine like terms: -7.211102551 + 2 = -5.211102551
r = -5.211102551

Simplifying
r = -5.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.211102551, -5.211102551}
Solution
r = {9.211102551, -5.211102551}

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