x^2-0.66x-2.8=0

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Solution for x^2-0.66x-2.8=0 equation: 


Simplifying
x2 + -0.66x + -2.8 = 0

Reorder the terms:
-2.8 + -0.66x + x2 = 0

Solving
-2.8 + -0.66x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + -0.66x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + -0.66x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + -0.66x + x2 = 0 + 2.8
-0.66x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
-0.66x + x2 = 2.8

The x term is -0.66x.  Take half its coefficient (-0.33).
Square it (0.1089) and add it to both sides.

Add '0.1089' to each side of the equation.
-0.66x + 0.1089 + x2 = 2.8 + 0.1089

Reorder the terms:
0.1089 + -0.66x + x2 = 2.8 + 0.1089

Combine like terms: 2.8 + 0.1089 = 2.9089
0.1089 + -0.66x + x2 = 2.9089

Factor a perfect square on the left side:
(x + -0.33)(x + -0.33) = 2.9089

Calculate the square root of the right side: 1.705549765

Break this problem into two subproblems by setting 
(x + -0.33) equal to 1.705549765 and -1.705549765.


Subproblem 1
x + -0.33 = 1.705549765

Simplifying
x + -0.33 = 1.705549765

Reorder the terms:
-0.33 + x = 1.705549765

Solving
-0.33 + x = 1.705549765

Solving for variable 'x'.

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

Add '0.33' to each side of the equation.
-0.33 + 0.33 + x = 1.705549765 + 0.33

Combine like terms: -0.33 + 0.33 = 0.00
0.00 + x = 1.705549765 + 0.33
x = 1.705549765 + 0.33

Combine like terms: 1.705549765 + 0.33 = 2.035549765
x = 2.035549765

Simplifying
x = 2.035549765


Subproblem 2
x + -0.33 = -1.705549765

Simplifying
x + -0.33 = -1.705549765

Reorder the terms:
-0.33 + x = -1.705549765

Solving
-0.33 + x = -1.705549765

Solving for variable 'x'.

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

Add '0.33' to each side of the equation.
-0.33 + 0.33 + x = -1.705549765 + 0.33

Combine like terms: -0.33 + 0.33 = 0.00
0.00 + x = -1.705549765 + 0.33
x = -1.705549765 + 0.33

Combine like terms: -1.705549765 + 0.33 = -1.375549765
x = -1.375549765

Simplifying
x = -1.375549765


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.035549765, -1.375549765}

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