.083x^2-.924x+1.846=0

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Solution for .083x^2-.924x+1.846=0 equation: 


Simplifying
0.083x2 + -0.924x + 1.846 = 0

Reorder the terms:
1.846 + -0.924x + 0.083x2 = 0

Solving
1.846 + -0.924x + 0.083x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.083'.
22.24096386 + -11.13253012x + x2 = 0

Move the constant term to the right:

Add '-22.24096386' to each side of the equation.
22.24096386 + -11.13253012x + -22.24096386 + x2 = 0 + -22.24096386

Reorder the terms:
22.24096386 + -22.24096386 + -11.13253012x + x2 = 0 + -22.24096386

Combine like terms: 22.24096386 + -22.24096386 = 0.00000000
0.00000000 + -11.13253012x + x2 = 0 + -22.24096386
-11.13253012x + x2 = 0 + -22.24096386

Combine like terms: 0 + -22.24096386 = -22.24096386
-11.13253012x + x2 = -22.24096386

The x term is -11.13253012x.  Take half its coefficient (-5.56626506).
Square it (30.98330672) and add it to both sides.

Add '30.98330672' to each side of the equation.
-11.13253012x + 30.98330672 + x2 = -22.24096386 + 30.98330672

Reorder the terms:
30.98330672 + -11.13253012x + x2 = -22.24096386 + 30.98330672

Combine like terms: -22.24096386 + 30.98330672 = 8.74234286
30.98330672 + -11.13253012x + x2 = 8.74234286

Factor a perfect square on the left side:
(x + -5.56626506)(x + -5.56626506) = 8.74234286

Calculate the square root of the right side: 2.956745315

Break this problem into two subproblems by setting 
(x + -5.56626506) equal to 2.956745315 and -2.956745315.


Subproblem 1
x + -5.56626506 = 2.956745315

Simplifying
x + -5.56626506 = 2.956745315

Reorder the terms:
-5.56626506 + x = 2.956745315

Solving
-5.56626506 + x = 2.956745315

Solving for variable 'x'.

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

Add '5.56626506' to each side of the equation.
-5.56626506 + 5.56626506 + x = 2.956745315 + 5.56626506

Combine like terms: -5.56626506 + 5.56626506 = 0.00000000
0.00000000 + x = 2.956745315 + 5.56626506
x = 2.956745315 + 5.56626506

Combine like terms: 2.956745315 + 5.56626506 = 8.523010375
x = 8.523010375

Simplifying
x = 8.523010375


Subproblem 2
x + -5.56626506 = -2.956745315

Simplifying
x + -5.56626506 = -2.956745315

Reorder the terms:
-5.56626506 + x = -2.956745315

Solving
-5.56626506 + x = -2.956745315

Solving for variable 'x'.

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

Add '5.56626506' to each side of the equation.
-5.56626506 + 5.56626506 + x = -2.956745315 + 5.56626506

Combine like terms: -5.56626506 + 5.56626506 = 0.00000000
0.00000000 + x = -2.956745315 + 5.56626506
x = -2.956745315 + 5.56626506

Combine like terms: -2.956745315 + 5.56626506 = 2.609519745
x = 2.609519745

Simplifying
x = 2.609519745


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.523010375, 2.609519745}

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