x[148201+x]=0.629

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Solution for x[148201+x]=0.629 equation: 


Simplifying
x[148201 + x] = 0.629
[148201 * x + x * x] = 0.629
[148201x + x2] = 0.629

Solving
148201x + x2 = 0.629

Solving for variable 'x'.

Reorder the terms:
-0.629 + 148201x + x2 = 0.629 + -0.629

Combine like terms: 0.629 + -0.629 = 0.000
-0.629 + 148201x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.629' to each side of the equation.
-0.629 + 148201x + 0.629 + x2 = 0.000 + 0.629

Reorder the terms:
-0.629 + 0.629 + 148201x + x2 = 0.000 + 0.629

Combine like terms: -0.629 + 0.629 = 0.000
0.000 + 148201x + x2 = 0.000 + 0.629
148201x + x2 = 0.000 + 0.629

Combine like terms: 0.000 + 0.629 = 0.629
148201x + x2 = 0.629

The x term is 148201x.  Take half its coefficient (74100.5).
Square it (5490884100) and add it to both sides.

Add '5490884100' to each side of the equation.
148201x + 5490884100 + x2 = 0.629 + 5490884100

Reorder the terms:
5490884100 + 148201x + x2 = 0.629 + 5490884100

Combine like terms: 0.629 + 5490884100 = 5490884100.629
5490884100 + 148201x + x2 = 5490884100.629

Factor a perfect square on the left side:
(x + 74100.5)(x + 74100.5) = 5490884100.629

Calculate the square root of the right side: 74100.500002557

Break this problem into two subproblems by setting 
(x + 74100.5) equal to 74100.500002557 and -74100.500002557.


Subproblem 1
x + 74100.5 = 74100.500002557

Simplifying
x + 74100.5 = 74100.500002557

Reorder the terms:
74100.5 + x = 74100.500002557

Solving
74100.5 + x = 74100.500002557

Solving for variable 'x'.

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

Add '-74100.5' to each side of the equation.
74100.5 + -74100.5 + x = 74100.500002557 + -74100.5

Combine like terms: 74100.5 + -74100.5 = 0.0
0.0 + x = 74100.500002557 + -74100.5
x = 74100.500002557 + -74100.5

Combine like terms: 74100.500002557 + -74100.5 = 0.000002557
x = 0.000002557

Simplifying
x = 0.000002557


Subproblem 2
x + 74100.5 = -74100.500002557

Simplifying
x + 74100.5 = -74100.500002557

Reorder the terms:
74100.5 + x = -74100.500002557

Solving
74100.5 + x = -74100.500002557

Solving for variable 'x'.

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

Add '-74100.5' to each side of the equation.
74100.5 + -74100.5 + x = -74100.500002557 + -74100.5

Combine like terms: 74100.5 + -74100.5 = 0.0
0.0 + x = -74100.500002557 + -74100.5
x = -74100.500002557 + -74100.5

Combine like terms: -74100.500002557 + -74100.5 = -148201.000002557
x = -148201.000002557

Simplifying
x = -148201.000002557


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.000002557, -148201.000002557}

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