(x^2+10+21094x-8)=0

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Solution for (x^2+10+21094x-8)=0 equation: 


Simplifying
(x2 + 10 + 21094x + -8) = 0

Reorder the terms:
(10 + -8 + 21094x + x2) = 0

Combine like terms: 10 + -8 = 2
(2 + 21094x + x2) = 0

Remove parenthesis around (2 + 21094x + x2)
2 + 21094x + x2 = 0

Solving
2 + 21094x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 21094x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 21094x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 21094x + x2 = 0 + -2
21094x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
21094x + x2 = -2

The x term is 21094x.  Take half its coefficient (10547).
Square it (111239209) and add it to both sides.

Add '111239209' to each side of the equation.
21094x + 111239209 + x2 = -2 + 111239209

Reorder the terms:
111239209 + 21094x + x2 = -2 + 111239209

Combine like terms: -2 + 111239209 = 111239207
111239209 + 21094x + x2 = 111239207

Factor a perfect square on the left side:
(x + 10547)(x + 10547) = 111239207

Calculate the square root of the right side: 10546.999905186

Break this problem into two subproblems by setting 
(x + 10547) equal to 10546.999905186 and -10546.999905186.


Subproblem 1
x + 10547 = 10546.999905186

Simplifying
x + 10547 = 10546.999905186

Reorder the terms:
10547 + x = 10546.999905186

Solving
10547 + x = 10546.999905186

Solving for variable 'x'.

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

Add '-10547' to each side of the equation.
10547 + -10547 + x = 10546.999905186 + -10547

Combine like terms: 10547 + -10547 = 0
0 + x = 10546.999905186 + -10547
x = 10546.999905186 + -10547

Combine like terms: 10546.999905186 + -10547 = -0.000094814
x = -0.000094814

Simplifying
x = -0.000094814


Subproblem 2
x + 10547 = -10546.999905186

Simplifying
x + 10547 = -10546.999905186

Reorder the terms:
10547 + x = -10546.999905186

Solving
10547 + x = -10546.999905186

Solving for variable 'x'.

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

Add '-10547' to each side of the equation.
10547 + -10547 + x = -10546.999905186 + -10547

Combine like terms: 10547 + -10547 = 0
0 + x = -10546.999905186 + -10547
x = -10546.999905186 + -10547

Combine like terms: -10546.999905186 + -10547 = -21093.999905186
x = -21093.999905186

Simplifying
x = -21093.999905186


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.000094814, -21093.999905186}

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