x^2-38.8571x=-370.514

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Solution for x^2-38.8571x=-370.514 equation: 


Simplifying
x2 + -38.8571x = -370.514

Reorder the terms:
-38.8571x + x2 = -370.514

Solving
-38.8571x + x2 = -370.514

Solving for variable 'x'.

Reorder the terms:
370.514 + -38.8571x + x2 = -370.514 + 370.514

Combine like terms: -370.514 + 370.514 = 0.000
370.514 + -38.8571x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '-370.514' to each side of the equation.
370.514 + -38.8571x + -370.514 + x2 = 0.000 + -370.514

Reorder the terms:
370.514 + -370.514 + -38.8571x + x2 = 0.000 + -370.514

Combine like terms: 370.514 + -370.514 = 0.000
0.000 + -38.8571x + x2 = 0.000 + -370.514
-38.8571x + x2 = 0.000 + -370.514

Combine like terms: 0.000 + -370.514 = -370.514
-38.8571x + x2 = -370.514

The x term is -38.8571x.  Take half its coefficient (-19.42855).
Square it (377.4685551) and add it to both sides.

Add '377.4685551' to each side of the equation.
-38.8571x + 377.4685551 + x2 = -370.514 + 377.4685551

Reorder the terms:
377.4685551 + -38.8571x + x2 = -370.514 + 377.4685551

Combine like terms: -370.514 + 377.4685551 = 6.9545551
377.4685551 + -38.8571x + x2 = 6.9545551

Factor a perfect square on the left side:
(x + -19.42855)(x + -19.42855) = 6.9545551

Calculate the square root of the right side: 2.637149048

Break this problem into two subproblems by setting 
(x + -19.42855) equal to 2.637149048 and -2.637149048.


Subproblem 1
x + -19.42855 = 2.637149048

Simplifying
x + -19.42855 = 2.637149048

Reorder the terms:
-19.42855 + x = 2.637149048

Solving
-19.42855 + x = 2.637149048

Solving for variable 'x'.

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

Add '19.42855' to each side of the equation.
-19.42855 + 19.42855 + x = 2.637149048 + 19.42855

Combine like terms: -19.42855 + 19.42855 = 0.00000
0.00000 + x = 2.637149048 + 19.42855
x = 2.637149048 + 19.42855

Combine like terms: 2.637149048 + 19.42855 = 22.065699048
x = 22.065699048

Simplifying
x = 22.065699048


Subproblem 2
x + -19.42855 = -2.637149048

Simplifying
x + -19.42855 = -2.637149048

Reorder the terms:
-19.42855 + x = -2.637149048

Solving
-19.42855 + x = -2.637149048

Solving for variable 'x'.

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

Add '19.42855' to each side of the equation.
-19.42855 + 19.42855 + x = -2.637149048 + 19.42855

Combine like terms: -19.42855 + 19.42855 = 0.00000
0.00000 + x = -2.637149048 + 19.42855
x = -2.637149048 + 19.42855

Combine like terms: -2.637149048 + 19.42855 = 16.791400952
x = 16.791400952

Simplifying
x = 16.791400952


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.065699048, 16.791400952}

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