0.610x^2-4.28x+2.93=0

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Solution for 0.610x^2-4.28x+2.93=0 equation: 


Simplifying
0.610x2 + -4.28x + 2.93 = 0

Reorder the terms:
2.93 + -4.28x + 0.610x2 = 0

Solving
2.93 + -4.28x + 0.610x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.610'.
4.803278689 + -7.016393443x + x2 = 0

Move the constant term to the right:

Add '-4.803278689' to each side of the equation.
4.803278689 + -7.016393443x + -4.803278689 + x2 = 0 + -4.803278689

Reorder the terms:
4.803278689 + -4.803278689 + -7.016393443x + x2 = 0 + -4.803278689

Combine like terms: 4.803278689 + -4.803278689 = 0.000000000
0.000000000 + -7.016393443x + x2 = 0 + -4.803278689
-7.016393443x + x2 = 0 + -4.803278689

Combine like terms: 0 + -4.803278689 = -4.803278689
-7.016393443x + x2 = -4.803278689

The x term is -7.016393443x.  Take half its coefficient (-3.508196722).
Square it (12.30744424) and add it to both sides.

Add '12.30744424' to each side of the equation.
-7.016393443x + 12.30744424 + x2 = -4.803278689 + 12.30744424

Reorder the terms:
12.30744424 + -7.016393443x + x2 = -4.803278689 + 12.30744424

Combine like terms: -4.803278689 + 12.30744424 = 7.504165551
12.30744424 + -7.016393443x + x2 = 7.504165551

Factor a perfect square on the left side:
(x + -3.508196722)(x + -3.508196722) = 7.504165551

Calculate the square root of the right side: 2.739373204

Break this problem into two subproblems by setting 
(x + -3.508196722) equal to 2.739373204 and -2.739373204.


Subproblem 1
x + -3.508196722 = 2.739373204

Simplifying
x + -3.508196722 = 2.739373204

Reorder the terms:
-3.508196722 + x = 2.739373204

Solving
-3.508196722 + x = 2.739373204

Solving for variable 'x'.

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

Add '3.508196722' to each side of the equation.
-3.508196722 + 3.508196722 + x = 2.739373204 + 3.508196722

Combine like terms: -3.508196722 + 3.508196722 = 0.000000000
0.000000000 + x = 2.739373204 + 3.508196722
x = 2.739373204 + 3.508196722

Combine like terms: 2.739373204 + 3.508196722 = 6.247569926
x = 6.247569926

Simplifying
x = 6.247569926


Subproblem 2
x + -3.508196722 = -2.739373204

Simplifying
x + -3.508196722 = -2.739373204

Reorder the terms:
-3.508196722 + x = -2.739373204

Solving
-3.508196722 + x = -2.739373204

Solving for variable 'x'.

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

Add '3.508196722' to each side of the equation.
-3.508196722 + 3.508196722 + x = -2.739373204 + 3.508196722

Combine like terms: -3.508196722 + 3.508196722 = 0.000000000
0.000000000 + x = -2.739373204 + 3.508196722
x = -2.739373204 + 3.508196722

Combine like terms: -2.739373204 + 3.508196722 = 0.768823518
x = 0.768823518

Simplifying
x = 0.768823518


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.247569926, 0.768823518}

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