4105.142-344.869x+x^2=

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Solution for 4105.142-344.869x+x^2= equation: 


Simplifying
4105.142 + -344.869x + x2 = 0

Solving
4105.142 + -344.869x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4105.142' to each side of the equation.
4105.142 + -344.869x + -4105.142 + x2 = 0 + -4105.142

Reorder the terms:
4105.142 + -4105.142 + -344.869x + x2 = 0 + -4105.142

Combine like terms: 4105.142 + -4105.142 = 0.000
0.000 + -344.869x + x2 = 0 + -4105.142
-344.869x + x2 = 0 + -4105.142

Combine like terms: 0 + -4105.142 = -4105.142
-344.869x + x2 = -4105.142

The x term is -344.869x.  Take half its coefficient (-172.4345).
Square it (29733.65679) and add it to both sides.

Add '29733.65679' to each side of the equation.
-344.869x + 29733.65679 + x2 = -4105.142 + 29733.65679

Reorder the terms:
29733.65679 + -344.869x + x2 = -4105.142 + 29733.65679

Combine like terms: -4105.142 + 29733.65679 = 25628.51479
29733.65679 + -344.869x + x2 = 25628.51479

Factor a perfect square on the left side:
(x + -172.4345)(x + -172.4345) = 25628.51479

Calculate the square root of the right side: 160.089083919

Break this problem into two subproblems by setting 
(x + -172.4345) equal to 160.089083919 and -160.089083919.


Subproblem 1
x + -172.4345 = 160.089083919

Simplifying
x + -172.4345 = 160.089083919

Reorder the terms:
-172.4345 + x = 160.089083919

Solving
-172.4345 + x = 160.089083919

Solving for variable 'x'.

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

Add '172.4345' to each side of the equation.
-172.4345 + 172.4345 + x = 160.089083919 + 172.4345

Combine like terms: -172.4345 + 172.4345 = 0.0000
0.0000 + x = 160.089083919 + 172.4345
x = 160.089083919 + 172.4345

Combine like terms: 160.089083919 + 172.4345 = 332.523583919
x = 332.523583919

Simplifying
x = 332.523583919


Subproblem 2
x + -172.4345 = -160.089083919

Simplifying
x + -172.4345 = -160.089083919

Reorder the terms:
-172.4345 + x = -160.089083919

Solving
-172.4345 + x = -160.089083919

Solving for variable 'x'.

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

Add '172.4345' to each side of the equation.
-172.4345 + 172.4345 + x = -160.089083919 + 172.4345

Combine like terms: -172.4345 + 172.4345 = 0.0000
0.0000 + x = -160.089083919 + 172.4345
x = -160.089083919 + 172.4345

Combine like terms: -160.089083919 + 172.4345 = 12.345416081
x = 12.345416081

Simplifying
x = 12.345416081


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {332.523583919, 12.345416081}

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