r^2+26r+29=0

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Solution for r^2+26r+29=0 equation: 


Simplifying
r2 + 26r + 29 = 0

Reorder the terms:
29 + 26r + r2 = 0

Solving
29 + 26r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + 26r + -29 + r2 = 0 + -29

Reorder the terms:
29 + -29 + 26r + r2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 26r + r2 = 0 + -29
26r + r2 = 0 + -29

Combine like terms: 0 + -29 = -29
26r + r2 = -29

The r term is 26r.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26r + 169 + r2 = -29 + 169

Reorder the terms:
169 + 26r + r2 = -29 + 169

Combine like terms: -29 + 169 = 140
169 + 26r + r2 = 140

Factor a perfect square on the left side:
(r + 13)(r + 13) = 140

Calculate the square root of the right side: 11.832159566

Break this problem into two subproblems by setting 
(r + 13) equal to 11.832159566 and -11.832159566.


Subproblem 1
r + 13 = 11.832159566

Simplifying
r + 13 = 11.832159566

Reorder the terms:
13 + r = 11.832159566

Solving
13 + r = 11.832159566

Solving for variable 'r'.

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

Add '-13' to each side of the equation.
13 + -13 + r = 11.832159566 + -13

Combine like terms: 13 + -13 = 0
0 + r = 11.832159566 + -13
r = 11.832159566 + -13

Combine like terms: 11.832159566 + -13 = -1.167840434
r = -1.167840434

Simplifying
r = -1.167840434


Subproblem 2
r + 13 = -11.832159566

Simplifying
r + 13 = -11.832159566

Reorder the terms:
13 + r = -11.832159566

Solving
13 + r = -11.832159566

Solving for variable 'r'.

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

Add '-13' to each side of the equation.
13 + -13 + r = -11.832159566 + -13

Combine like terms: 13 + -13 = 0
0 + r = -11.832159566 + -13
r = -11.832159566 + -13

Combine like terms: -11.832159566 + -13 = -24.832159566
r = -24.832159566

Simplifying
r = -24.832159566


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-1.167840434, -24.832159566}

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