x^2-4x+3.66=0

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Solution for x^2-4x+3.66=0 equation:


Simplifying
x2 + -4x + 3.66 = 0

Reorder the terms:
3.66 + -4x + x2 = 0

Solving
3.66 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3.66' to each side of the equation.
3.66 + -4x + -3.66 + x2 = 0 + -3.66

Reorder the terms:
3.66 + -3.66 + -4x + x2 = 0 + -3.66

Combine like terms: 3.66 + -3.66 = 0.00
0.00 + -4x + x2 = 0 + -3.66
-4x + x2 = 0 + -3.66

Combine like terms: 0 + -3.66 = -3.66
-4x + x2 = -3.66

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -3.66 + 4

Reorder the terms:
4 + -4x + x2 = -3.66 + 4

Combine like terms: -3.66 + 4 = 0.34
4 + -4x + x2 = 0.34

Factor a perfect square on the left side:
(x + -2)(x + -2) = 0.34

Calculate the square root of the right side: 0.583095189

Break this problem into two subproblems by setting 
(x + -2) equal to 0.583095189 and -0.583095189.


Subproblem 1
x + -2 = 0.583095189

Simplifying
x + -2 = 0.583095189

Reorder the terms:
-2 + x = 0.583095189

Solving
-2 + x = 0.583095189

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 0.583095189 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0.583095189 + 2
x = 0.583095189 + 2

Combine like terms: 0.583095189 + 2 = 2.583095189
x = 2.583095189

Simplifying
x = 2.583095189


Subproblem 2
x + -2 = -0.583095189

Simplifying
x + -2 = -0.583095189

Reorder the terms:
-2 + x = -0.583095189

Solving
-2 + x = -0.583095189

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -0.583095189 + 2

Combine like terms: -2 + 2 = 0
0 + x = -0.583095189 + 2
x = -0.583095189 + 2

Combine like terms: -0.583095189 + 2 = 1.416904811
x = 1.416904811

Simplifying
x = 1.416904811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.583095189, 1.416904811}

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