r^2-14r-98=0

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Solution for r^2-14r-98=0 equation: 


Simplifying
r2 + -14r + -98 = 0

Reorder the terms:
-98 + -14r + r2 = 0

Solving
-98 + -14r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + -14r + 98 + r2 = 0 + 98

Reorder the terms:
-98 + 98 + -14r + r2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + -14r + r2 = 0 + 98
-14r + r2 = 0 + 98

Combine like terms: 0 + 98 = 98
-14r + r2 = 98

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 = 98 + 49

Reorder the terms:
49 + -14r + r2 = 98 + 49

Combine like terms: 98 + 49 = 147
49 + -14r + r2 = 147

Factor a perfect square on the left side:
(r + -7)(r + -7) = 147

Calculate the square root of the right side: 12.124355653

Break this problem into two subproblems by setting 
(r + -7) equal to 12.124355653 and -12.124355653.


Subproblem 1
r + -7 = 12.124355653

Simplifying
r + -7 = 12.124355653

Reorder the terms:
-7 + r = 12.124355653

Solving
-7 + r = 12.124355653

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 = 12.124355653 + 7

Combine like terms: -7 + 7 = 0
0 + r = 12.124355653 + 7
r = 12.124355653 + 7

Combine like terms: 12.124355653 + 7 = 19.124355653
r = 19.124355653

Simplifying
r = 19.124355653


Subproblem 2
r + -7 = -12.124355653

Simplifying
r + -7 = -12.124355653

Reorder the terms:
-7 + r = -12.124355653

Solving
-7 + r = -12.124355653

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 = -12.124355653 + 7

Combine like terms: -7 + 7 = 0
0 + r = -12.124355653 + 7
r = -12.124355653 + 7

Combine like terms: -12.124355653 + 7 = -5.124355653
r = -5.124355653

Simplifying
r = -5.124355653


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {19.124355653, -5.124355653}

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