a^2-a-3.75=0

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Solution for a^2-a-3.75=0 equation: 


Simplifying
a2 + -1a + -3.75 = 0

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

Solving
-3.75 + -1a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

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 -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 = 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 = 2.5
a = 2.5

Simplifying
a = 2.5


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 = -1.5
a = -1.5

Simplifying
a = -1.5


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

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