38.54x^2-17126.92x-40196.79=0

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Solution for 38.54x^2-17126.92x-40196.79=0 equation: 


Simplifying
38.54x2 + -17126.92x + -40196.79 = 0

Reorder the terms:
-40196.79 + -17126.92x + 38.54x2 = 0

Solving
-40196.79 + -17126.92x + 38.54x2 = 0

Solving for variable 'x'.

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

Divide each side by '38.54'.
-1042.988843 + -444.3933576x + x2 = 0

Move the constant term to the right:

Add '1042.988843' to each side of the equation.
-1042.988843 + -444.3933576x + 1042.988843 + x2 = 0 + 1042.988843

Reorder the terms:
-1042.988843 + 1042.988843 + -444.3933576x + x2 = 0 + 1042.988843

Combine like terms: -1042.988843 + 1042.988843 = 0.000000
0.000000 + -444.3933576x + x2 = 0 + 1042.988843
-444.3933576x + x2 = 0 + 1042.988843

Combine like terms: 0 + 1042.988843 = 1042.988843
-444.3933576x + x2 = 1042.988843

The x term is -444.3933576x.  Take half its coefficient (-222.1966788).
Square it (49371.36407) and add it to both sides.

Add '49371.36407' to each side of the equation.
-444.3933576x + 49371.36407 + x2 = 1042.988843 + 49371.36407

Reorder the terms:
49371.36407 + -444.3933576x + x2 = 1042.988843 + 49371.36407

Combine like terms: 1042.988843 + 49371.36407 = 50414.352913
49371.36407 + -444.3933576x + x2 = 50414.352913

Factor a perfect square on the left side:
(x + -222.1966788)(x + -222.1966788) = 50414.352913

Calculate the square root of the right side: 224.531407409

Break this problem into two subproblems by setting 
(x + -222.1966788) equal to 224.531407409 and -224.531407409.


Subproblem 1
x + -222.1966788 = 224.531407409

Simplifying
x + -222.1966788 = 224.531407409

Reorder the terms:
-222.1966788 + x = 224.531407409

Solving
-222.1966788 + x = 224.531407409

Solving for variable 'x'.

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

Add '222.1966788' to each side of the equation.
-222.1966788 + 222.1966788 + x = 224.531407409 + 222.1966788

Combine like terms: -222.1966788 + 222.1966788 = 0.0000000
0.0000000 + x = 224.531407409 + 222.1966788
x = 224.531407409 + 222.1966788

Combine like terms: 224.531407409 + 222.1966788 = 446.728086209
x = 446.728086209

Simplifying
x = 446.728086209


Subproblem 2
x + -222.1966788 = -224.531407409

Simplifying
x + -222.1966788 = -224.531407409

Reorder the terms:
-222.1966788 + x = -224.531407409

Solving
-222.1966788 + x = -224.531407409

Solving for variable 'x'.

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

Add '222.1966788' to each side of the equation.
-222.1966788 + 222.1966788 + x = -224.531407409 + 222.1966788

Combine like terms: -222.1966788 + 222.1966788 = 0.0000000
0.0000000 + x = -224.531407409 + 222.1966788
x = -224.531407409 + 222.1966788

Combine like terms: -224.531407409 + 222.1966788 = -2.334728609
x = -2.334728609

Simplifying
x = -2.334728609


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {446.728086209, -2.334728609}

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