x^2-3.3x+0.48=0

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Solution for x^2-3.3x+0.48=0 equation: 


Simplifying
x2 + -3.3x + 0.48 = 0

Reorder the terms:
0.48 + -3.3x + x2 = 0

Solving
0.48 + -3.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.48' to each side of the equation.
0.48 + -3.3x + -0.48 + x2 = 0 + -0.48

Reorder the terms:
0.48 + -0.48 + -3.3x + x2 = 0 + -0.48

Combine like terms: 0.48 + -0.48 = 0.00
0.00 + -3.3x + x2 = 0 + -0.48
-3.3x + x2 = 0 + -0.48

Combine like terms: 0 + -0.48 = -0.48
-3.3x + x2 = -0.48

The x term is -3.3x.  Take half its coefficient (-1.65).
Square it (2.7225) and add it to both sides.

Add '2.7225' to each side of the equation.
-3.3x + 2.7225 + x2 = -0.48 + 2.7225

Reorder the terms:
2.7225 + -3.3x + x2 = -0.48 + 2.7225

Combine like terms: -0.48 + 2.7225 = 2.2425
2.7225 + -3.3x + x2 = 2.2425

Factor a perfect square on the left side:
(x + -1.65)(x + -1.65) = 2.2425

Calculate the square root of the right side: 1.497497913

Break this problem into two subproblems by setting 
(x + -1.65) equal to 1.497497913 and -1.497497913.


Subproblem 1
x + -1.65 = 1.497497913

Simplifying
x + -1.65 = 1.497497913

Reorder the terms:
-1.65 + x = 1.497497913

Solving
-1.65 + x = 1.497497913

Solving for variable 'x'.

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

Add '1.65' to each side of the equation.
-1.65 + 1.65 + x = 1.497497913 + 1.65

Combine like terms: -1.65 + 1.65 = 0.00
0.00 + x = 1.497497913 + 1.65
x = 1.497497913 + 1.65

Combine like terms: 1.497497913 + 1.65 = 3.147497913
x = 3.147497913

Simplifying
x = 3.147497913


Subproblem 2
x + -1.65 = -1.497497913

Simplifying
x + -1.65 = -1.497497913

Reorder the terms:
-1.65 + x = -1.497497913

Solving
-1.65 + x = -1.497497913

Solving for variable 'x'.

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

Add '1.65' to each side of the equation.
-1.65 + 1.65 + x = -1.497497913 + 1.65

Combine like terms: -1.65 + 1.65 = 0.00
0.00 + x = -1.497497913 + 1.65
x = -1.497497913 + 1.65

Combine like terms: -1.497497913 + 1.65 = 0.152502087
x = 0.152502087

Simplifying
x = 0.152502087


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.147497913, 0.152502087}

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