x^2-714x+42194=0

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Solution for x^2-714x+42194=0 equation: 


Simplifying
x2 + -714x + 42194 = 0

Reorder the terms:
42194 + -714x + x2 = 0

Solving
42194 + -714x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-42194' to each side of the equation.
42194 + -714x + -42194 + x2 = 0 + -42194

Reorder the terms:
42194 + -42194 + -714x + x2 = 0 + -42194

Combine like terms: 42194 + -42194 = 0
0 + -714x + x2 = 0 + -42194
-714x + x2 = 0 + -42194

Combine like terms: 0 + -42194 = -42194
-714x + x2 = -42194

The x term is -714x.  Take half its coefficient (-357).
Square it (127449) and add it to both sides.

Add '127449' to each side of the equation.
-714x + 127449 + x2 = -42194 + 127449

Reorder the terms:
127449 + -714x + x2 = -42194 + 127449

Combine like terms: -42194 + 127449 = 85255
127449 + -714x + x2 = 85255

Factor a perfect square on the left side:
(x + -357)(x + -357) = 85255

Calculate the square root of the right side: 291.984588634

Break this problem into two subproblems by setting 
(x + -357) equal to 291.984588634 and -291.984588634.


Subproblem 1
x + -357 = 291.984588634

Simplifying
x + -357 = 291.984588634

Reorder the terms:
-357 + x = 291.984588634

Solving
-357 + x = 291.984588634

Solving for variable 'x'.

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

Add '357' to each side of the equation.
-357 + 357 + x = 291.984588634 + 357

Combine like terms: -357 + 357 = 0
0 + x = 291.984588634 + 357
x = 291.984588634 + 357

Combine like terms: 291.984588634 + 357 = 648.984588634
x = 648.984588634

Simplifying
x = 648.984588634


Subproblem 2
x + -357 = -291.984588634

Simplifying
x + -357 = -291.984588634

Reorder the terms:
-357 + x = -291.984588634

Solving
-357 + x = -291.984588634

Solving for variable 'x'.

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

Add '357' to each side of the equation.
-357 + 357 + x = -291.984588634 + 357

Combine like terms: -357 + 357 = 0
0 + x = -291.984588634 + 357
x = -291.984588634 + 357

Combine like terms: -291.984588634 + 357 = 65.015411366
x = 65.015411366

Simplifying
x = 65.015411366


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {648.984588634, 65.015411366}

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