53.3x^2-44.64x+8.528=0

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Solution for 53.3x^2-44.64x+8.528=0 equation: 


Simplifying
53.3x2 + -44.64x + 8.528 = 0

Reorder the terms:
8.528 + -44.64x + 53.3x2 = 0

Solving
8.528 + -44.64x + 53.3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
53.3 the coefficient of the squared term: 

Divide each side by '53.3'.
0.16 + -0.8375234522x + x2 = 0

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -0.8375234522x + -0.16 + x2 = 0 + -0.16

Reorder the terms:
0.16 + -0.16 + -0.8375234522x + x2 = 0 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -0.8375234522x + x2 = 0 + -0.16
-0.8375234522x + x2 = 0 + -0.16

Combine like terms: 0 + -0.16 = -0.16
-0.8375234522x + x2 = -0.16

The x term is -0.8375234522x.  Take half its coefficient (-0.4187617261).
Square it (0.1753613832) and add it to both sides.

Add '0.1753613832' to each side of the equation.
-0.8375234522x + 0.1753613832 + x2 = -0.16 + 0.1753613832

Reorder the terms:
0.1753613832 + -0.8375234522x + x2 = -0.16 + 0.1753613832

Combine like terms: -0.16 + 0.1753613832 = 0.0153613832
0.1753613832 + -0.8375234522x + x2 = 0.0153613832

Factor a perfect square on the left side:
(x + -0.4187617261)(x + -0.4187617261) = 0.0153613832

Calculate the square root of the right side: 0.123941047

Break this problem into two subproblems by setting 
(x + -0.4187617261) equal to 0.123941047 and -0.123941047.


Subproblem 1
x + -0.4187617261 = 0.123941047

Simplifying
x + -0.4187617261 = 0.123941047

Reorder the terms:
-0.4187617261 + x = 0.123941047

Solving
-0.4187617261 + x = 0.123941047

Solving for variable 'x'.

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

Add '0.4187617261' to each side of the equation.
-0.4187617261 + 0.4187617261 + x = 0.123941047 + 0.4187617261

Combine like terms: -0.4187617261 + 0.4187617261 = 0.0000000000
0.0000000000 + x = 0.123941047 + 0.4187617261
x = 0.123941047 + 0.4187617261

Combine like terms: 0.123941047 + 0.4187617261 = 0.5427027731
x = 0.5427027731

Simplifying
x = 0.5427027731


Subproblem 2
x + -0.4187617261 = -0.123941047

Simplifying
x + -0.4187617261 = -0.123941047

Reorder the terms:
-0.4187617261 + x = -0.123941047

Solving
-0.4187617261 + x = -0.123941047

Solving for variable 'x'.

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

Add '0.4187617261' to each side of the equation.
-0.4187617261 + 0.4187617261 + x = -0.123941047 + 0.4187617261

Combine like terms: -0.4187617261 + 0.4187617261 = 0.0000000000
0.0000000000 + x = -0.123941047 + 0.4187617261
x = -0.123941047 + 0.4187617261

Combine like terms: -0.123941047 + 0.4187617261 = 0.2948206791
x = 0.2948206791

Simplifying
x = 0.2948206791


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5427027731, 0.2948206791}

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