14.4=a+a^2

Solution for 14.4=a+a^2 equation:

Simplifying
14.4 = a + a2

Solving
14.4 = a + a2

Solving for variable 'a'.

Reorder the terms:
14.4 + -1a + -1a2 = a + -1a + a2 + -1a2

Combine like terms: a + -1a = 0
14.4 + -1a + -1a2 = 0 + a2 + -1a2
14.4 + -1a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
14.4 + -1a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-14.4 + a + a2 = 0

Move the constant term to the right:

Add '14.4' to each side of the equation.
-14.4 + a + 14.4 + a2 = 0 + 14.4

Reorder the terms:
-14.4 + 14.4 + a + a2 = 0 + 14.4

Combine like terms: -14.4 + 14.4 = 0.0
0.0 + a + a2 = 0 + 14.4
a + a2 = 0 + 14.4

Combine like terms: 0 + 14.4 = 14.4
a + a2 = 14.4

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + a2 = 14.4 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + a2 = 14.4 + 0.25

Combine like terms: 14.4 + 0.25 = 14.65
1.25 + a2 = 14.65

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 14.65

Calculate the square root of the right side: 3.827531842

Break this problem into two subproblems by setting 
(a + 0.5) equal to 3.827531842 and -3.827531842.

Subproblem 1
a + 0.5 = 3.827531842

Simplifying
a + 0.5 = 3.827531842

Reorder the terms:
0.5 + a = 3.827531842

Solving
0.5 + a = 3.827531842

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 3.827531842 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 3.827531842 + -0.5
a = 3.827531842 + -0.5

Combine like terms: 3.827531842 + -0.5 = 3.327531842
a = 3.327531842

Simplifying
a = 3.327531842

Subproblem 2
a + 0.5 = -3.827531842

Simplifying
a + 0.5 = -3.827531842

Reorder the terms:
0.5 + a = -3.827531842

Solving
0.5 + a = -3.827531842

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -3.827531842 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -3.827531842 + -0.5
a = -3.827531842 + -0.5

Combine like terms: -3.827531842 + -0.5 = -4.327531842
a = -4.327531842

Simplifying
a = -4.327531842

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.327531842, -4.327531842}