2r^2+2r-14=0

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Solution for 2r^2+2r-14=0 equation: 


Simplifying
2r2 + 2r + -14 = 0

Reorder the terms:
-14 + 2r + 2r2 = 0

Solving
-14 + 2r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + r + r2) = 0

Ignore the factor 2.

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

Simplifying
-7 + r + r2 = 0

Solving
-7 + r + r2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
r + 0.25 + r2 = 7 + 0.25

Reorder the terms:
0.25 + r + r2 = 7 + 0.25

Combine like terms: 7 + 0.25 = 7.25
0.25 + r + r2 = 7.25

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(r + 0.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
r + 0.5 = 2.692582404

Simplifying
r + 0.5 = 2.692582404

Reorder the terms:
0.5 + r = 2.692582404

Solving
0.5 + r = 2.692582404

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 2.692582404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 2.692582404 + -0.5
r = 2.692582404 + -0.5

Combine like terms: 2.692582404 + -0.5 = 2.192582404
r = 2.192582404

Simplifying
r = 2.192582404


Subproblem 2
r + 0.5 = -2.692582404

Simplifying
r + 0.5 = -2.692582404

Reorder the terms:
0.5 + r = -2.692582404

Solving
0.5 + r = -2.692582404

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -2.692582404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -2.692582404 + -0.5
r = -2.692582404 + -0.5

Combine like terms: -2.692582404 + -0.5 = -3.192582404
r = -3.192582404

Simplifying
r = -3.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.192582404, -3.192582404}
Solution
r = {2.192582404, -3.192582404}

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