2a+11.5=a^2+0.25

Solution for 2a+11.5=a^2+0.25 equation:

Simplifying
2a + 11.5 = a2 + 0.25

Reorder the terms:
11.5 + 2a = a2 + 0.25

Reorder the terms:
11.5 + 2a = 0.25 + a2

Solving
11.5 + 2a = 0.25 + a2

Solving for variable 'a'.

Reorder the terms:
11.5 + -0.25 + 2a + -1a2 = 0.25 + a2 + -0.25 + -1a2

Combine like terms: 11.5 + -0.25 = 11.25
11.25 + 2a + -1a2 = 0.25 + a2 + -0.25 + -1a2

Reorder the terms:
11.25 + 2a + -1a2 = 0.25 + -0.25 + a2 + -1a2

Combine like terms: 0.25 + -0.25 = 0.00
11.25 + 2a + -1a2 = 0.00 + a2 + -1a2
11.25 + 2a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
11.25 + 2a + -1a2 = 0

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

Divide each side by '-1'.
-11.25 + -2a + a2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -2a + 11.25 + a2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -2a + a2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -2a + a2 = 0 + 11.25
-2a + a2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-2a + a2 = 11.25

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = 11.25 + 1

Reorder the terms:
1 + -2a + a2 = 11.25 + 1

Combine like terms: 11.25 + 1 = 12.25
1 + -2a + a2 = 12.25

Factor a perfect square on the left side:
(a + -1)(a + -1) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(a + -1) equal to 3.5 and -3.5.

Subproblem 1
a + -1 = 3.5

Simplifying
a + -1 = 3.5

Reorder the terms:
-1 + a = 3.5

Solving
-1 + a = 3.5

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = 3.5 + 1

Combine like terms: -1 + 1 = 0
0 + a = 3.5 + 1
a = 3.5 + 1

Combine like terms: 3.5 + 1 = 4.5
a = 4.5

Simplifying
a = 4.5

Subproblem 2
a + -1 = -3.5

Simplifying
a + -1 = -3.5

Reorder the terms:
-1 + a = -3.5

Solving
-1 + a = -3.5

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = -3.5 + 1

Combine like terms: -1 + 1 = 0
0 + a = -3.5 + 1
a = -3.5 + 1

Combine like terms: -3.5 + 1 = -2.5
a = -2.5

Simplifying
a = -2.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.5, -2.5}