-2r^2-28r+58=0

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Solution for -2r^2-28r+58=0 equation: 


Simplifying
-2r2 + -28r + 58 = 0

Reorder the terms:
58 + -28r + -2r2 = 0

Solving
58 + -28r + -2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + -14r + -1r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(29 + -14r + -1r2)' equal to zero and attempt to solve:

Simplifying
29 + -14r + -1r2 = 0

Solving
29 + -14r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-29 + 14r + r2 = 0

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 14r + 29 + r2 = 0 + 29

Reorder the terms:
-29 + 29 + 14r + r2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 14r + r2 = 0 + 29
14r + r2 = 0 + 29

Combine like terms: 0 + 29 = 29
14r + r2 = 29

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 = 29 + 49

Reorder the terms:
49 + 14r + r2 = 29 + 49

Combine like terms: 29 + 49 = 78
49 + 14r + r2 = 78

Factor a perfect square on the left side:
(r + 7)(r + 7) = 78

Calculate the square root of the right side: 8.831760866

Break this problem into two subproblems by setting 
(r + 7) equal to 8.831760866 and -8.831760866.


Subproblem 1
r + 7 = 8.831760866

Simplifying
r + 7 = 8.831760866

Reorder the terms:
7 + r = 8.831760866

Solving
7 + r = 8.831760866

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 = 8.831760866 + -7

Combine like terms: 7 + -7 = 0
0 + r = 8.831760866 + -7
r = 8.831760866 + -7

Combine like terms: 8.831760866 + -7 = 1.831760866
r = 1.831760866

Simplifying
r = 1.831760866


Subproblem 2
r + 7 = -8.831760866

Simplifying
r + 7 = -8.831760866

Reorder the terms:
7 + r = -8.831760866

Solving
7 + r = -8.831760866

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 = -8.831760866 + -7

Combine like terms: 7 + -7 = 0
0 + r = -8.831760866 + -7
r = -8.831760866 + -7

Combine like terms: -8.831760866 + -7 = -15.831760866
r = -15.831760866

Simplifying
r = -15.831760866


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.831760866, -15.831760866}
Solution
r = {1.831760866, -15.831760866}

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