r^2+25r=7

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Solution for r^2+25r=7 equation: 


Simplifying
r2 + 25r = 7

Reorder the terms:
25r + r2 = 7

Solving
25r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + 25r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 25r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 25r + 7 + r2 = 0 + 7

Reorder the terms:
-7 + 7 + 25r + r2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 25r + r2 = 0 + 7
25r + r2 = 0 + 7

Combine like terms: 0 + 7 = 7
25r + r2 = 7

The r term is 25r.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25r + 156.25 + r2 = 7 + 156.25

Reorder the terms:
156.25 + 25r + r2 = 7 + 156.25

Combine like terms: 7 + 156.25 = 163.25
156.25 + 25r + r2 = 163.25

Factor a perfect square on the left side:
(r + 12.5)(r + 12.5) = 163.25

Calculate the square root of the right side: 12.776932339

Break this problem into two subproblems by setting 
(r + 12.5) equal to 12.776932339 and -12.776932339.


Subproblem 1
r + 12.5 = 12.776932339

Simplifying
r + 12.5 = 12.776932339

Reorder the terms:
12.5 + r = 12.776932339

Solving
12.5 + r = 12.776932339

Solving for variable 'r'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + r = 12.776932339 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + r = 12.776932339 + -12.5
r = 12.776932339 + -12.5

Combine like terms: 12.776932339 + -12.5 = 0.276932339
r = 0.276932339

Simplifying
r = 0.276932339


Subproblem 2
r + 12.5 = -12.776932339

Simplifying
r + 12.5 = -12.776932339

Reorder the terms:
12.5 + r = -12.776932339

Solving
12.5 + r = -12.776932339

Solving for variable 'r'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + r = -12.776932339 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + r = -12.776932339 + -12.5
r = -12.776932339 + -12.5

Combine like terms: -12.776932339 + -12.5 = -25.276932339
r = -25.276932339

Simplifying
r = -25.276932339


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.276932339, -25.276932339}

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