2180000x^2=0.275-2x

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Solution for 2180000x^2=0.275-2x equation: 


Simplifying
2180000x2 = 0.275 + -2x

Solving
2180000x2 = 0.275 + -2x

Solving for variable 'x'.

Reorder the terms:
-0.275 + 2x + 2180000x2 = 0.275 + -2x + -0.275 + 2x

Reorder the terms:
-0.275 + 2x + 2180000x2 = 0.275 + -0.275 + -2x + 2x

Combine like terms: 0.275 + -0.275 = 0.000
-0.275 + 2x + 2180000x2 = 0.000 + -2x + 2x
-0.275 + 2x + 2180000x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-0.275 + 2x + 2180000x2 = 0

Begin completing the square.  Divide all terms by
2180000 the coefficient of the squared term: 

Divide each side by '2180000'.
-0.000000126146789 + 0.0000009174311927x + x2 = 0

Move the constant term to the right:

Add '0.000000126146789' to each side of the equation.
-0.000000126146789 + 0.0000009174311927x + 0.000000126146789 + x2 = 0 + 0.000000126146789

Reorder the terms:
-0.000000126146789 + 0.000000126146789 + 0.0000009174311927x + x2 = 0 + 0.000000126146789

Combine like terms: -0.000000126146789 + 0.000000126146789 = 0.000000000000000
0.000000000000000 + 0.0000009174311927x + x2 = 0 + 0.000000126146789
0.0000009174311927x + x2 = 0 + 0.000000126146789

Combine like terms: 0 + 0.000000126146789 = 0.000000126146789
0.0000009174311927x + x2 = 0.000000126146789

The x term is 0.0000009174311927x.  Take half its coefficient (0.0000004587155964).
Square it (0.0000000000002104199984) and add it to both sides.

Add '0.0000000000002104199984' to each side of the equation.
0.0000009174311927x + 0.0000000000002104199984 + x2 = 0.000000126146789 + 0.0000000000002104199984

Reorder the terms:
0.0000000000002104199984 + 0.0000009174311927x + x2 = 0.000000126146789 + 0.0000000000002104199984

Combine like terms: 0.000000126146789 + 0.0000000000002104199984 = 0.0000001261469994199984
0.0000000000002104199984 + 0.0000009174311927x + x2 = 0.0000001261469994199984

Factor a perfect square on the left side:
(x + 0.0000004587155964)(x + 0.0000004587155964) = 0.0000001261469994199984

Calculate the square root of the right side: 0.000355172

Break this problem into two subproblems by setting 
(x + 0.0000004587155964) equal to 0.000355172 and -0.000355172.


Subproblem 1
x + 0.0000004587155964 = 0.000355172

Simplifying
x + 0.0000004587155964 = 0.000355172

Reorder the terms:
0.0000004587155964 + x = 0.000355172

Solving
0.0000004587155964 + x = 0.000355172

Solving for variable 'x'.

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

Add '-0.0000004587155964' to each side of the equation.
0.0000004587155964 + -0.0000004587155964 + x = 0.000355172 + -0.0000004587155964

Combine like terms: 0.0000004587155964 + -0.0000004587155964 = 0.0000000000000000
0.0000000000000000 + x = 0.000355172 + -0.0000004587155964
x = 0.000355172 + -0.0000004587155964

Combine like terms: 0.000355172 + -0.0000004587155964 = 0.0003547132844036
x = 0.0003547132844036

Simplifying
x = 0.0003547132844036


Subproblem 2
x + 0.0000004587155964 = -0.000355172

Simplifying
x + 0.0000004587155964 = -0.000355172

Reorder the terms:
0.0000004587155964 + x = -0.000355172

Solving
0.0000004587155964 + x = -0.000355172

Solving for variable 'x'.

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

Add '-0.0000004587155964' to each side of the equation.
0.0000004587155964 + -0.0000004587155964 + x = -0.000355172 + -0.0000004587155964

Combine like terms: 0.0000004587155964 + -0.0000004587155964 = 0.0000000000000000
0.0000000000000000 + x = -0.000355172 + -0.0000004587155964
x = -0.000355172 + -0.0000004587155964

Combine like terms: -0.000355172 + -0.0000004587155964 = -0.0003556307155964
x = -0.0003556307155964

Simplifying
x = -0.0003556307155964


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0003547132844036, -0.0003556307155964}

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