x^2=103258.49-58.6x

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Solution for x^2=103258.49-58.6x equation: 


Simplifying
x2 = 103258.49 + -58.6x

Solving
x2 = 103258.49 + -58.6x

Solving for variable 'x'.

Reorder the terms:
-103258.49 + 58.6x + x2 = 103258.49 + -58.6x + -103258.49 + 58.6x

Reorder the terms:
-103258.49 + 58.6x + x2 = 103258.49 + -103258.49 + -58.6x + 58.6x

Combine like terms: 103258.49 + -103258.49 = 0.00
-103258.49 + 58.6x + x2 = 0.00 + -58.6x + 58.6x
-103258.49 + 58.6x + x2 = -58.6x + 58.6x

Combine like terms: -58.6x + 58.6x = 0.0
-103258.49 + 58.6x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '103258.49' to each side of the equation.
-103258.49 + 58.6x + 103258.49 + x2 = 0.0 + 103258.49

Reorder the terms:
-103258.49 + 103258.49 + 58.6x + x2 = 0.0 + 103258.49

Combine like terms: -103258.49 + 103258.49 = 0.00
0.00 + 58.6x + x2 = 0.0 + 103258.49
58.6x + x2 = 0.0 + 103258.49

Combine like terms: 0.0 + 103258.49 = 103258.49
58.6x + x2 = 103258.49

The x term is 58.6x.  Take half its coefficient (29.3).
Square it (858.49) and add it to both sides.

Add '858.49' to each side of the equation.
58.6x + 858.49 + x2 = 103258.49 + 858.49

Reorder the terms:
858.49 + 58.6x + x2 = 103258.49 + 858.49

Combine like terms: 103258.49 + 858.49 = 104116.98
858.49 + 58.6x + x2 = 104116.98

Factor a perfect square on the left side:
(x + 29.3)(x + 29.3) = 104116.98

Calculate the square root of the right side: 322.67162875

Break this problem into two subproblems by setting 
(x + 29.3) equal to 322.67162875 and -322.67162875.


Subproblem 1
x + 29.3 = 322.67162875

Simplifying
x + 29.3 = 322.67162875

Reorder the terms:
29.3 + x = 322.67162875

Solving
29.3 + x = 322.67162875

Solving for variable 'x'.

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

Add '-29.3' to each side of the equation.
29.3 + -29.3 + x = 322.67162875 + -29.3

Combine like terms: 29.3 + -29.3 = 0.0
0.0 + x = 322.67162875 + -29.3
x = 322.67162875 + -29.3

Combine like terms: 322.67162875 + -29.3 = 293.37162875
x = 293.37162875

Simplifying
x = 293.37162875


Subproblem 2
x + 29.3 = -322.67162875

Simplifying
x + 29.3 = -322.67162875

Reorder the terms:
29.3 + x = -322.67162875

Solving
29.3 + x = -322.67162875

Solving for variable 'x'.

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

Add '-29.3' to each side of the equation.
29.3 + -29.3 + x = -322.67162875 + -29.3

Combine like terms: 29.3 + -29.3 = 0.0
0.0 + x = -322.67162875 + -29.3
x = -322.67162875 + -29.3

Combine like terms: -322.67162875 + -29.3 = -351.97162875
x = -351.97162875

Simplifying
x = -351.97162875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {293.37162875, -351.97162875}

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