x^2+10x+21=12257001

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Solution for x^2+10x+21=12257001 equation: 


Simplifying
x2 + 10x + 21 = 12257001

Reorder the terms:
21 + 10x + x2 = 12257001

Solving
21 + 10x + x2 = 12257001

Solving for variable 'x'.

Reorder the terms:
21 + -12257001 + 10x + x2 = 12257001 + -12257001

Combine like terms: 21 + -12257001 = -12256980
-12256980 + 10x + x2 = 12257001 + -12257001

Combine like terms: 12257001 + -12257001 = 0
-12256980 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12256980' to each side of the equation.
-12256980 + 10x + 12256980 + x2 = 0 + 12256980

Reorder the terms:
-12256980 + 12256980 + 10x + x2 = 0 + 12256980

Combine like terms: -12256980 + 12256980 = 0
0 + 10x + x2 = 0 + 12256980
10x + x2 = 0 + 12256980

Combine like terms: 0 + 12256980 = 12256980
10x + x2 = 12256980

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 12256980 + 25

Reorder the terms:
25 + 10x + x2 = 12256980 + 25

Combine like terms: 12256980 + 25 = 12257005
25 + 10x + x2 = 12257005

Factor a perfect square on the left side:
(x + 5)(x + 5) = 12257005

Calculate the square root of the right side: 3501.000571265

Break this problem into two subproblems by setting 
(x + 5) equal to 3501.000571265 and -3501.000571265.


Subproblem 1
x + 5 = 3501.000571265

Simplifying
x + 5 = 3501.000571265

Reorder the terms:
5 + x = 3501.000571265

Solving
5 + x = 3501.000571265

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 3501.000571265 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3501.000571265 + -5
x = 3501.000571265 + -5

Combine like terms: 3501.000571265 + -5 = 3496.000571265
x = 3496.000571265

Simplifying
x = 3496.000571265


Subproblem 2
x + 5 = -3501.000571265

Simplifying
x + 5 = -3501.000571265

Reorder the terms:
5 + x = -3501.000571265

Solving
5 + x = -3501.000571265

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -3501.000571265 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3501.000571265 + -5
x = -3501.000571265 + -5

Combine like terms: -3501.000571265 + -5 = -3506.000571265
x = -3506.000571265

Simplifying
x = -3506.000571265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3496.000571265, -3506.000571265}

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