r^2+14r-25=0

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Solution for r^2+14r-25=0 equation: 


Simplifying
r2 + 14r + -25 = 0

Reorder the terms:
-25 + 14r + r2 = 0

Solving
-25 + 14r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 14r + 25 + r2 = 0 + 25

Reorder the terms:
-25 + 25 + 14r + r2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 14r + r2 = 0 + 25
14r + r2 = 0 + 25

Combine like terms: 0 + 25 = 25
14r + r2 = 25

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 = 25 + 49

Reorder the terms:
49 + 14r + r2 = 25 + 49

Combine like terms: 25 + 49 = 74
49 + 14r + r2 = 74

Factor a perfect square on the left side:
(r + 7)(r + 7) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(r + 7) equal to 8.602325267 and -8.602325267.


Subproblem 1
r + 7 = 8.602325267

Simplifying
r + 7 = 8.602325267

Reorder the terms:
7 + r = 8.602325267

Solving
7 + r = 8.602325267

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 = 8.602325267 + -7

Combine like terms: 7 + -7 = 0
0 + r = 8.602325267 + -7
r = 8.602325267 + -7

Combine like terms: 8.602325267 + -7 = 1.602325267
r = 1.602325267

Simplifying
r = 1.602325267


Subproblem 2
r + 7 = -8.602325267

Simplifying
r + 7 = -8.602325267

Reorder the terms:
7 + r = -8.602325267

Solving
7 + r = -8.602325267

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 = -8.602325267 + -7

Combine like terms: 7 + -7 = 0
0 + r = -8.602325267 + -7
r = -8.602325267 + -7

Combine like terms: -8.602325267 + -7 = -15.602325267
r = -15.602325267

Simplifying
r = -15.602325267


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.602325267, -15.602325267}

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