a+4=a^2+0.25

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Solution for a+4=a^2+0.25 equation: 


Simplifying
a + 4 = a2 + 0.25

Reorder the terms:
4 + a = a2 + 0.25

Reorder the terms:
4 + a = 0.25 + a2

Solving
4 + a = 0.25 + a2

Solving for variable 'a'.

Reorder the terms:
4 + -0.25 + a + -1a2 = 0.25 + a2 + -0.25 + -1a2

Combine like terms: 4 + -0.25 = 3.75
3.75 + a + -1a2 = 0.25 + a2 + -0.25 + -1a2

Reorder the terms:
3.75 + a + -1a2 = 0.25 + -0.25 + a2 + -1a2

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

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

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

Divide each side by '-1'.
-3.75 + -1a + a2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -1a + 3.75 + a2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -1a + a2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -1a + a2 = 0 + 3.75
-1a + a2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-1a + a2 = 3.75

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.
-1a + 0.25 + a2 = 3.75 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 3.75 + 0.25

Combine like terms: 3.75 + 0.25 = 4
0.25 + -1a + a2 = 4

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(a + 0.5) equal to 2 and -2.


Subproblem 1
a + 0.5 = 2

Simplifying
a + 0.5 = 2

Reorder the terms:
0.5 + a = 2

Solving
0.5 + a = 2

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 = 2 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 2 + -0.5
a = 2 + -0.5

Combine like terms: 2 + -0.5 = 1.5
a = 1.5

Simplifying
a = 1.5


Subproblem 2
a + 0.5 = -2

Simplifying
a + 0.5 = -2

Reorder the terms:
0.5 + a = -2

Solving
0.5 + a = -2

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 = -2 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -2 + -0.5
a = -2 + -0.5

Combine like terms: -2 + -0.5 = -2.5
a = -2.5

Simplifying
a = -2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.5, -2.5}

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