a^2-a-4.25=0

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Solution for a^2-a-4.25=0 equation: 


Simplifying
a2 + -1a + -4.25 = 0

Reorder the terms:
-4.25 + -1a + a2 = 0

Solving
-4.25 + -1a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + -1a + 4.25 + a2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + -1a + a2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + -1a + a2 = 0 + 4.25
-1a + a2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
-1a + a2 = 4.25

The a term is -1a.  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 = 4.25 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 4.25 + 0.25

Combine like terms: 4.25 + 0.25 = 4.5
0.25 + -1a + a2 = 4.5

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(a + -0.5) equal to 2.121320344 and -2.121320344.


Subproblem 1
a + -0.5 = 2.121320344

Simplifying
a + -0.5 = 2.121320344

Reorder the terms:
-0.5 + a = 2.121320344

Solving
-0.5 + a = 2.121320344

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 = 2.121320344 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = 2.121320344 + 0.5
a = 2.121320344 + 0.5

Combine like terms: 2.121320344 + 0.5 = 2.621320344
a = 2.621320344

Simplifying
a = 2.621320344


Subproblem 2
a + -0.5 = -2.121320344

Simplifying
a + -0.5 = -2.121320344

Reorder the terms:
-0.5 + a = -2.121320344

Solving
-0.5 + a = -2.121320344

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 = -2.121320344 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = -2.121320344 + 0.5
a = -2.121320344 + 0.5

Combine like terms: -2.121320344 + 0.5 = -1.621320344
a = -1.621320344

Simplifying
a = -1.621320344


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.621320344, -1.621320344}

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