3r^2+42r-21=0

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Solution for 3r^2+42r-21=0 equation: 


Simplifying
3r2 + 42r + -21 = 0

Reorder the terms:
-21 + 42r + 3r2 = 0

Solving
-21 + 42r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 14r + r2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + 14r + r2)' equal to zero and attempt to solve:

Simplifying
-7 + 14r + r2 = 0

Solving
-7 + 14r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 14r + 7 + r2 = 0 + 7

Reorder the terms:
-7 + 7 + 14r + r2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 14r + r2 = 0 + 7
14r + r2 = 0 + 7

Combine like terms: 0 + 7 = 7
14r + r2 = 7

The r term is 14r.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14r + 49 + r2 = 7 + 49

Reorder the terms:
49 + 14r + r2 = 7 + 49

Combine like terms: 7 + 49 = 56
49 + 14r + r2 = 56

Factor a perfect square on the left side:
(r + 7)(r + 7) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(r + 7) equal to 7.483314774 and -7.483314774.


Subproblem 1
r + 7 = 7.483314774

Simplifying
r + 7 = 7.483314774

Reorder the terms:
7 + r = 7.483314774

Solving
7 + r = 7.483314774

Solving for variable 'r'.

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

Add '-7' to each side of the equation.
7 + -7 + r = 7.483314774 + -7

Combine like terms: 7 + -7 = 0
0 + r = 7.483314774 + -7
r = 7.483314774 + -7

Combine like terms: 7.483314774 + -7 = 0.483314774
r = 0.483314774

Simplifying
r = 0.483314774


Subproblem 2
r + 7 = -7.483314774

Simplifying
r + 7 = -7.483314774

Reorder the terms:
7 + r = -7.483314774

Solving
7 + r = -7.483314774

Solving for variable 'r'.

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

Add '-7' to each side of the equation.
7 + -7 + r = -7.483314774 + -7

Combine like terms: 7 + -7 = 0
0 + r = -7.483314774 + -7
r = -7.483314774 + -7

Combine like terms: -7.483314774 + -7 = -14.483314774
r = -14.483314774

Simplifying
r = -14.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.483314774, -14.483314774}
Solution
r = {0.483314774, -14.483314774}

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