x^2-1752x+58384=0

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Solution for x^2-1752x+58384=0 equation: 


Simplifying
x2 + -1752x + 58384 = 0

Reorder the terms:
58384 + -1752x + x2 = 0

Solving
58384 + -1752x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-58384' to each side of the equation.
58384 + -1752x + -58384 + x2 = 0 + -58384

Reorder the terms:
58384 + -58384 + -1752x + x2 = 0 + -58384

Combine like terms: 58384 + -58384 = 0
0 + -1752x + x2 = 0 + -58384
-1752x + x2 = 0 + -58384

Combine like terms: 0 + -58384 = -58384
-1752x + x2 = -58384

The x term is -1752x.  Take half its coefficient (-876).
Square it (767376) and add it to both sides.

Add '767376' to each side of the equation.
-1752x + 767376 + x2 = -58384 + 767376

Reorder the terms:
767376 + -1752x + x2 = -58384 + 767376

Combine like terms: -58384 + 767376 = 708992
767376 + -1752x + x2 = 708992

Factor a perfect square on the left side:
(x + -876)(x + -876) = 708992

Calculate the square root of the right side: 842.016626914

Break this problem into two subproblems by setting 
(x + -876) equal to 842.016626914 and -842.016626914.


Subproblem 1
x + -876 = 842.016626914

Simplifying
x + -876 = 842.016626914

Reorder the terms:
-876 + x = 842.016626914

Solving
-876 + x = 842.016626914

Solving for variable 'x'.

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

Add '876' to each side of the equation.
-876 + 876 + x = 842.016626914 + 876

Combine like terms: -876 + 876 = 0
0 + x = 842.016626914 + 876
x = 842.016626914 + 876

Combine like terms: 842.016626914 + 876 = 1718.016626914
x = 1718.016626914

Simplifying
x = 1718.016626914


Subproblem 2
x + -876 = -842.016626914

Simplifying
x + -876 = -842.016626914

Reorder the terms:
-876 + x = -842.016626914

Solving
-876 + x = -842.016626914

Solving for variable 'x'.

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

Add '876' to each side of the equation.
-876 + 876 + x = -842.016626914 + 876

Combine like terms: -876 + 876 = 0
0 + x = -842.016626914 + 876
x = -842.016626914 + 876

Combine like terms: -842.016626914 + 876 = 33.983373086
x = 33.983373086

Simplifying
x = 33.983373086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1718.016626914, 33.983373086}

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