0=a^2+14a+36

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Solution for 0=a^2+14a+36 equation: 


Simplifying
0 = a2 + 14a + 36

Reorder the terms:
0 = 36 + 14a + a2

Solving
0 = 36 + 14a + a2

Solving for variable 'a'.

Combine like terms: 0 + -36 = -36
-36 + -14a + -1a2 = 36 + 14a + a2 + -36 + -14a + -1a2

Reorder the terms:
-36 + -14a + -1a2 = 36 + -36 + 14a + -14a + a2 + -1a2

Combine like terms: 36 + -36 = 0
-36 + -14a + -1a2 = 0 + 14a + -14a + a2 + -1a2
-36 + -14a + -1a2 = 14a + -14a + a2 + -1a2

Combine like terms: 14a + -14a = 0
-36 + -14a + -1a2 = 0 + a2 + -1a2
-36 + -14a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-36 + -14a + -1a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(36 + 14a + a2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(36 + 14a + a2)' equal to zero and attempt to solve:

Simplifying
36 + 14a + a2 = 0

Solving
36 + 14a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 14a + -36 + a2 = 0 + -36

Reorder the terms:
36 + -36 + 14a + a2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 14a + a2 = 0 + -36
14a + a2 = 0 + -36

Combine like terms: 0 + -36 = -36
14a + a2 = -36

The a term is 14a.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14a + 49 + a2 = -36 + 49

Reorder the terms:
49 + 14a + a2 = -36 + 49

Combine like terms: -36 + 49 = 13
49 + 14a + a2 = 13

Factor a perfect square on the left side:
(a + 7)(a + 7) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(a + 7) equal to 3.605551275 and -3.605551275.


Subproblem 1
a + 7 = 3.605551275

Simplifying
a + 7 = 3.605551275

Reorder the terms:
7 + a = 3.605551275

Solving
7 + a = 3.605551275

Solving for variable 'a'.

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

Add '-7' to each side of the equation.
7 + -7 + a = 3.605551275 + -7

Combine like terms: 7 + -7 = 0
0 + a = 3.605551275 + -7
a = 3.605551275 + -7

Combine like terms: 3.605551275 + -7 = -3.394448725
a = -3.394448725

Simplifying
a = -3.394448725


Subproblem 2
a + 7 = -3.605551275

Simplifying
a + 7 = -3.605551275

Reorder the terms:
7 + a = -3.605551275

Solving
7 + a = -3.605551275

Solving for variable 'a'.

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

Add '-7' to each side of the equation.
7 + -7 + a = -3.605551275 + -7

Combine like terms: 7 + -7 = 0
0 + a = -3.605551275 + -7
a = -3.605551275 + -7

Combine like terms: -3.605551275 + -7 = -10.605551275
a = -10.605551275

Simplifying
a = -10.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-3.394448725, -10.605551275}
Solution
a = {-3.394448725, -10.605551275}

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