a(a-1)=2.75

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Solution for a(a-1)=2.75 equation: 


Simplifying
a(a + -1) = 2.75

Reorder the terms:
a(-1 + a) = 2.75
(-1 * a + a * a) = 2.75
(-1a + a2) = 2.75

Solving
-1a + a2 = 2.75

Solving for variable 'a'.

Reorder the terms:
-2.75 + -1a + a2 = 2.75 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
-2.75 + -1a + a2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -1a + 2.75 + a2 = 0.00 + 2.75

Reorder the terms:
-2.75 + 2.75 + -1a + a2 = 0.00 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -1a + a2 = 0.00 + 2.75
-1a + a2 = 0.00 + 2.75

Combine like terms: 0.00 + 2.75 = 2.75
-1a + a2 = 2.75

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 = 2.75 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 2.75 + 0.25

Combine like terms: 2.75 + 0.25 = 3
0.25 + -1a + a2 = 3

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(a + -0.5) equal to 1.732050808 and -1.732050808.


Subproblem 1
a + -0.5 = 1.732050808

Simplifying
a + -0.5 = 1.732050808

Reorder the terms:
-0.5 + a = 1.732050808

Solving
-0.5 + a = 1.732050808

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 = 1.732050808 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = 1.732050808 + 0.5
a = 1.732050808 + 0.5

Combine like terms: 1.732050808 + 0.5 = 2.232050808
a = 2.232050808

Simplifying
a = 2.232050808


Subproblem 2
a + -0.5 = -1.732050808

Simplifying
a + -0.5 = -1.732050808

Reorder the terms:
-0.5 + a = -1.732050808

Solving
-0.5 + a = -1.732050808

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 = -1.732050808 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = -1.732050808 + 0.5
a = -1.732050808 + 0.5

Combine like terms: -1.732050808 + 0.5 = -1.232050808
a = -1.232050808

Simplifying
a = -1.232050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.232050808, -1.232050808}

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